Systems and methods for ofdm duobinary transmission

ABSTRACT

A method of modulating a series of input digital symbols of a first modulation scheme is provided. The method is implemented by a transmitter and includes receiving a sequential series of samples of the digital symbols in a first domain of the first modulation scheme. The first domain is one of the time domain and the frequency domain. The method further includes determining a dual of the first modulation scheme. The dual has a second modulation scheme in a second domain that is different from the first domain the second domain is the other of the time domain and the frequency domain. The method further includes applying a 90 degree rotational operation to the second modulation scheme to generate a rotational modulation format, modulating the series of digital symbols with the generated rotational modulation format, and outputting the modulated series of digital symbols to a receiver.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of U.S. patent applicationSer. No. 15/833,832, filed Dec. 6, 2017, which claims the benefit of andpriority to U.S. Provisional Patent Application Ser. No. 62/447,661,filed Jan. 18, 2017, U.S. Provisional Patent Application Ser. No.62/447,665, filed Jan. 18, 2017, U.S. Provisional Patent ApplicationSer. No. 62/447,702, filed Jan. 18, 2017, U.S. Provisional PatentApplication Ser. No. 62/469,962, filed Mar. 10, 2017, and also to U.S.Provisional Patent Application Ser. No. 62/512,913, filed May 31, 2017.This application also claims the benefit of and priority to U.S.Provisional Patent Application Ser. No. 62/447,584, filed Jan. 18, 2017,U.S. Provisional Patent Application Ser. No. 62/453,710, filed Feb. 2,2017, and U.S. Provisional Patent Application Ser. No. 62/546,119, filedAug. 16, 2017. The disclosures of all of these prior applications areherein incorporated by reference in their entireties.

BACKGROUND

The field of the disclosure relates generally to digital transmissionsystems, and more particularly, to multi-carrier wired, wireless, andoptical digital transmission systems.

Conventional digital transmission systems typically include both linearand non-linear distortion. However, for the purposes of the followingdiscussion, use of the term “distortion” is generally intended to referto linear distortion only. Conventional digital transmission systemsalso utilize symbols with coefficients, either in the time domain (TD)or frequency domain (FD), which are generally complex-value sequences.That is, the coefficients of the complex symbols typically include botha real component and an imaginary component, or alternatively, amagnitude and a phase value. Time and frequency domains are related, andthe two domains are duals of each other. That is, for a plot or asequence of numerical values, it must be known whether to observe theplotted numbers as time domain or frequency domain values.

This distinction is of particular significance when consideringmulti-carrier (MC) digital transmissions, such as with orthogonalfrequency division multiplexing (OFDM) and orthogonal frequency divisionmultiple access (OFDMA) transmissions. OFDM symbols, for example, whenplotted, appear as discrete values in the frequency domain, but looklike random noise in the time domain. In contrast, if a transmission issingle carrier (SC), its symbols can be viewed as discrete values in thetime domain, but look like random noise in the frequency domain. Thus,multi-carrier and single carrier transmissions are viewed in differentdomains.

One type of distortion that is known to severely affect digitaltransmissions is multipath. Multipath linear distortion is sometimesreferred to as “echoes,” “ghosts,” or “dispersion.” An example of anecho distortion is shown in FIG. 1A. FIG. 1A is a schematic illustrationdepicting a conventional transmission system 100. System 100 includes atransmitter 102 with a transmitting antenna 104 and a receiver 106 witha receiving antenna 108. Transmitter 102 modulates a baseband signalonto a carrier, thereby forming an RF signal 110 for communication overa signal path 112 between transmitter 102 and receiver 106. Data oversignal path 112 includes telephony, computer code, file data, networkdata, internet, world wide web (WWW), entertainment video, video phone,security alarm signals, etc. The data may be widely broadcast, orintended for only the single receiver 106. Signal path 112 includes (i)a direct path portion 114, and (ii) an echo path portion 116 thatreflects off of a reflecting object 118. Data traveling over direct pathportion 114 results in a direct signal portion 120 at receiver 106, anddata traveling over echo path portion 116 results in an echo signalportion 122 at receiver 106. Direct signal portion 120 and echo signalportion are collectively received by receiver 106 as a received signal124.

Thus, the presence of echoes from reflections (e.g., from reflectingobject 118) causes received signal 124 to be distorted by the presenceof echo signal portion 122 combined with a direct signal portion 120. Insome cases, direct path portion 114 may be blocked by an obstruction 126between transmitter 102 and receiver 106, and the only signal receptionpossible will be from echo signal portion 122 over echo path portion116. In many cases, the received signal includes multiple echo signals.If the frequency response of the signal path 112 is measured, thepresence of a strong echo will cause ripples in the magnitude of theresponse, where the reciprocal of the frequency difference between peaksis the time delay of the echo from path 116, relative to the directsignal 120.

On wired signal paths, echoes may alternatively occur from impedancemismatches within coaxial networks. With multipath linear distortion,one or more copies of the original signal—typically with a delay andattenuation—are added to the original signal. On wireless signal paths,the multipath linear distortion, and therefore the attenuated anddelayed copies, may be caused by signals reflecting from structures,such as buildings, water towers, etc. In the example of radiatedtransmissions such as received broadcast analog television pictures, themultipath linear distortion may appear as additional fainter imagessuperimposed on the intended image, along with a typical delay relativeto the intended image received over a direct transmission path.

On single mode fiber optic cable using coherent optical signals, thetransmission characteristics are different relative to RF (sub-100 GHz)wired and wireless signal paths. For example, a 1550 nm wavelength laserhas an optical frequency of 193e12 Hz. In single mode glass fiber, animpairment called Chromatic Dispersion (CD) is encountered, which issimilar to group delay encountered, typically from filters, at muchlower wired and wireless frequencies. Signals at different frequencies(optical wavelengths) travel at different speeds down the fiber opticcable and this linear distortion needs to be equalized to minimizeinter-symbol interference (ISI). This impairment becomes more severewith increasing bandwidth and more severe with longer fiber optic cablespans. This type of signal interference is different from echoes, whichare not typically encountered on fiber optic transport media. Coaxialcables and free space, on the other hand, experience virtually no groupdelay (chromatic dispersion). Thus, CD is created by differentwavelengths of a signal traveling at different speeds, whereas echoesare reflected copies of the same signal.

On optical fiber, different polarizations can be used for simultaneoustransmission of two different signals, but because fiber cores sometimeshave elliptical shapes, as opposed to round shapes, signals withdifferent polarizations travel at different rates, resulting in animpairment that must be removed at the receiver. Satellites andmicrowave towers also use vertical and horizontal polarizations forsignals propagating in free space, but free space propagation does notexperience polarization distortions. In some conventional OFDMA andsingle-carrier frequency-division multiple-access (SC-FDMA) systems,overlapping signals from multiple transmitters are combined frommultiple transmitters at RF frequencies. At optical frequencies,however, these overlapping signal techniques experienced optical beatinterference (OBI) problem unless the optical signal phase purity ishigh. Therefore, echo problems are generally encountered on wired andwireless channels, but not on fiber optic cable (e.g., due to use ofangled connectors).

In the case of digital transmissions, mild multipath distortion willincrease the bit error rate (BER) in the presence of random noise orother additive impairments, and may thus be corrected, whereasun-equalized severe multipath distortion, on the other hand, may renderthe received data useless for further processing at the receiver end.Other types of linear distortions, such as a non-flat frequency responseor a group delay, may also affect or impair digital transmissions. Thesetypes of distortions may result from imperfect filters and/or amplifiertilt.

Some conventional techniques have been utilized to eliminate, or atleast equalize, multipath linear distortion in the time domain orfrequency domain. One conventional time domain technique utilizes anadaptive equalizer to correct for multipath distortion. The adaptiveequalizer sums a received distorted signal with a delayed version of thedistorted signal, in order to cancel the received echoes. Thiscancellation process is referred to as equalization, or “de-ghosting.”Conventional adaptive equalization schemes sometimes employ a filterarchitecture such as a finite impulse response (FIR) filter, whichutilizes a number of taps (either hardware or software) that areconfigured to execute a multiply-accumulate operation, and programscoefficients in the adaptive equalizer to cancel received echoes. Suchprogramming may utilize a particular reference signal, also referred toas a training signal or “ghost-canceling” signal, so that the programmedcoefficients are computed as an inverse of the channel response. Thefrequency and the impulse response of the channel may also be determinedas intermediate steps, and, in the time domain, tap coefficients arecomputed as the reciprocal of the impulse response. In some instances,the adaptive equalizer is programmed using blind equalizationtechniques. An exemplary FIR filter architecture is disclosed in U.S.Pat. No. 5,886,749, which is incorporated by reference herein.

Echoes on cable lines can come in two varieties: single recursion andmultiple (infinite) recursion. An infinite recursion occurs, forexample, by an echo tunnel as a signal bounces back and forth in thetunnel, getting weaker on each pass. FIG. 1B is a graphical illustrationdepicting examples of conventional time domain plots 128 for a multiplerecursion 130 and a single recursion 132 on an echo signal path, andrespective adaptive equalizer solutions (impulse response) 134implemented to correct the encountered recursion 130 or 132. As shown inillustration 128, the adaptive equalizer solution 134 _(M) that correctsmultiple recursion echo 130 though, is itself a single recursion. Incontrast, where the main signal path experiences single recursion 132(e.g., as can happen with two signal paths), the adaptive equalizersolution 134 _(S) that corrects single recursion echo 132 though, is amultiple recursion. In the conventional systems, multiple recursionsolution 134 _(M) requires more taps, or more time, than would singlerecursion solution 134 _(S) to remove an echo. If the echo is stronger,even more taps, with significant energy, are required.

Conventional adaptive equalization techniques, however, aresignificantly limited with respect to complex signals that requireprocessing of a large number of coefficients (e.g., greater than 8 or64). Because the FIR filter utilizes linear convolution, the rate ofrequired computations increases as the product of the number of taps,multiplied by the clocking speed of the taps. For hardware-implementedtaps, a large number of coefficients will significantly increase thecost and size of the physical structure that performs the adaptiveequalization. For software-implemented taps, an exponential increasewill significantly increase the required processing speed of theprogramming that performs computations. Large quantities of taps areparticularly necessary where, for example, the clock frequency of theequalizer is high, and where a received echo is long.

Some conventional techniques attempt to solve the multiple-computationalproblems associated with adaptive equalization by taking a receiveddistorted signal in the time domain, separating the time domain signalinto blocks, and then transforming the blocks into the frequency domain,such as through use of a fast Fourier transform (FFT). The transformedblocks thus become sets of frequency domain subcarriers, and eachfrequency domain subcarrier may then be multiplied by a single complexcoefficient to remove the associated linear distortion. This process isknown as frequency domain equalization (FDE).

Once the linear distortion is removed, the frequency domain blocks areconverted back into time domain blocks. A problem occurs, however, ifthe blocks are contaminated with foreign or extraneous energy, such asmight occur from echo energy transporting distortion from a previousblock. Conventional systems address this energy transportation problemthrough use of cyclic prefixes (CP), which are a set of time domainsymbols copied from the end of the block and pasted onto the front ofthe block.

FIG. 2A is a graphical illustration of a time domain signal 200 of aconventional OFDM transmission 202 having a cyclic prefix 204, utilizedin accordance with transmission system 100, FIG. 1A. Typically, an OFDMcarrier signal is the sum of one or more OFDM symbols, each symbol madeup of a plurality of orthogonal subcarriers, and with baseband data oneach subcarrier being independently modulated. In an embodiment, OFDMtransmission 202 is a carrier signal transmitted using technology suchas the Data Over Cable Service Interface Specification (DOCSIS), version3.1, or one or more of many known and burgeoning wireless standards. Asdescribed above, OFDM implements a plurality of different subcarriers,all of which are harmonics of a fundamental, to obtain orthogonality.

DOCSIS specifications conventionally utilize OFDM for downstream signalsand OFDMA for upstream signals. OFDM and OFDMA are complimentary. OFDMis typically used in the downstream transmission where there is onetransmitter (e.g., a Cable Modem Termination System (CMTS)) sendinginformation to multiple receivers (e.g., cable modems). OFDMA istypically used in the upstream transmission where there are multipletransmitters (e.g., the cable modems) transmitting to one receiver(e.g., the CMTS). The cyclic prefix is therefore commonly used in bothOFDM and OFDMA.

The cyclic prefix functions as a “guard time” that separates databursts, and allows any micro-reflection from one burst to die out beforethe next burst is received, thereby eliminating interference from oneblock to the next. The cyclic prefix is therefore consideredparticularly essential over an HFC network, where reflections frequentlyoccur. Reflections are often created by impedance mismatches on the HFCnetwork and result from a number of issues, including manufacturingtolerances of passive hardware such as taps, power inserters, andsplitter, active hardware such as amplifiers, and connectors. Combinedmultiple micro-reflections therefore, create linear distortions, whichcause a number of impairments to signal transmission, includingamplitude ripple (standing waves), group delay ripple, inter-symbolinterference, and degraded modulation error ratio (MER) on digitalsignals transmitted on the HFC network. For a conventional multicarrierequalization processes, the cyclic prefix should be longer than any echoin the signal path. Accordingly, various durations of cyclic prefixesare utilized to accommodate a variety of echo delays in the HFC network,thereby significantly increasing the overhead of the network, butwithout carrying any useful customer information in the transmission ofthe cyclic prefix.

OFDM transmission 202 includes, for example, first harmonic subcarrier206, second harmonic subcarrier 208, third harmonic subcarrier 210, andfourth harmonic subcarrier 212. For ease of explanation, only four suchsubcarriers of OFDM transmission 202 are illustrated, but typically,many more subcarriers exist. Each of the harmonically-relatedsubcarriers 206, 208, 210, 212 may have different magnitude and phasevalues. When all four subcarriers 206, 208, 210, 212 are combined, orsummed, for transmission, the summed result is a single composite signal214.

Orthogonality allows each of the original subcarriers to be separated atthe receiver (e.g., receiver 106, FIG. 1), such as with utilization ofFourier processes. That is, a discrete Fourier transform (e.g., an FFT)converts a set of time domain values into frequency domain values, andan inverse discrete Fourier transform (e.g., an IFFT) converts frequencydomain values into time domain values. The larger the transform, thegreater is the efficiency improvement by using an FFT, as opposed to asimple discrete Fourier transform. The FFT block sizes may beefficiently implemented with a block size of radix 2 (2{circumflex over( )}n, where n is an integer), such as 256, or 1024, but other efficienttransform block sizes are possible. Cyclic prefix 204 is created bycopying symbols from an end region 216 (shown shaded in gray) ofcomposite signal 214, and pasting the copied signals onto the beginningregion thereof as a guard interval. Cyclic prefix 204 thus allowscircular convolution or FDE to be performed on OFDM transmission 202,without suffering interference from a previous OFDM block if there is anecho on the channel. However, for this example, it is assumed that theecho is shorter than cyclic prefix 204.

FIG. 2B is a graphical illustration of a frequency domain signal 218 ofOFDM transmission 202, FIG. 2A. That is, frequency domain signal 218represents a spectral plot of OFDM transmission 202 in the frequencydomain. Frequency domain signal 218 may be obtained by performing adiscrete Fourier transform or an FFT on composite time domain signal214, FIG. 2A. As illustrated in FIG. 2B, each of time domain harmonicsubcarriers 206, 208, 210, 212 has a respective frequency domaincomponent subcarrier 220, 222, 224, 226, each having both a magnitudeand a phase value. Under these conventional techniques, OFDMtransmissions may be viewed in either the time domain or the frequencydomain. However, composite signal 214 appears noise-like, or random inthe time domain, which is problematic for multiple-carrier symbols. Incomparison, some single-carrier symbols, such as single-carrierfrequency-division multiple-access (SC-FDMA) can also be viewed eitherin the time domain or the frequency domain, but such single-carriersymbols resemble noise when viewed in the frequency domain. Accordingly,it is desirable to develop systems and methods capable of receiving,equalizing, and utilizing the same multiple-carrier or multiple-accesssymbols in both the time domain and the frequency domain.

Cyclic prefixes provide block-to-block isolation, and thus transmissionof digital information is often performed with blocks of data. Someconventional systems use linear code, such as a Reed-Solomon code orLow-Density Parity Check (LDPC) codes, for purposes of forward errorcorrection (FEC), which allows a percentage of erred symbols to becorrected by the code. Use of cyclic prefixes, however, requiresadditional resources to transmit the extra data that constitutes thecyclic prefix. The required cyclic prefix data reduces the bandwidthefficiency of transmissions, thereby limiting the amount of data thatcan be transmitted within a given frequency band, while also requiringadditional power and decreasing the battery life of system components.Moreover, as described above, cyclic prefixes are not completelyeffective in the case where the cyclic prefix portion of time domaindata is shorter than the length, or duration, of a received echo.

BRIEF SUMMARY

In an embodiment, a signal equalizing receiver is configured to capturea plurality of OFDM symbols transmitted over a signal path adding lineardistortion to the plurality of OFDM symbols, and form the plurality ofcaptured OFDM symbols into an overlapped compound data block. Thecompound data block includes at least one pseudo-extension in additionto payload data from at least one of the plurality of OFDM symbols. Thereceiver is further configured to process the overlapped compound datablock with one of (i) a circular convolution having an inverse channelresponse in the time domain, and (ii) a frequency domain equalization inthe frequency domain, to produce an equalized compound block, anddiscard at least one end portion of the equalized compound block toproduce a narrow equalized block. The at least one end portioncorresponds with the at least one pseudo-extension, and the narrowequalized block corresponds with the payload data. The receiver isfurther configured to cascade two or more narrow equalized blocks toform a de-ghosted signal stream of the plurality of OFDM symbols. Theplurality of OFDM symbols includes one or more of an OFDM transmissionand an OFDMA transmission. The plurality of OFDM symbols furtherincludes one or more of a cyclic prefix and no cyclic prefix. A lengthof the at least one pseudo extension is different than a length of thecyclic prefix.

In an embodiment, a digital transmission receiver has a processor and amemory. The receiver is configured to receive a digital signaltransmission from a signal path including a plurality of data blockshaving linear distortion, determine, from the signal path of the digitalsignal transmission, a duration of at least one reflection of thedigital signal transmission on the digital signal path, and attach apseudo-extension to a first data block of the plurality of data blocks.The length of the pseudo-extension in the time domain is greater thanthe duration of the at least one reflection. The receiver is furtherconfigured to process the first data block, together with thepseudo-extension attached thereto, to remove linear distortion from thefirst data block, and discard the processed pseudo-extension from theprocessed first data block after the linear distortion has been removed.

In an embodiment, a digital transmission system includes a transmitterconfigured to transmit orthogonal frequency-division multiplexing (OFDM)symbols having no cyclic prefix attached thereto, a receiver forreceiving the transmitted OFDM symbols from the transmitter, and asignal path for communicating the transmitted OFDM symbols from thetransmitter to the receiver. The OFDM symbols received by the receiverinclude linear distortion from the signal path, and the receiver isconfigured to process the received OFDM symbols and linear distortionusing an overlapped circular convolution function to produce equalizedOFDM symbols.

In an embodiment, a digital transmission system includes a transmitterconfigured to transmit orthogonal frequency-division multiplexing (OFDM)symbols having no cyclic prefix attached thereto, a receiver forreceiving the transmitted OFDM symbols from the transmitter, and asignal path for communicating the transmitted OFDM symbols from thetransmitter to the receiver. The OFDM symbols received by the receiverinclude linear distortion from the signal path, and the receiver isconfigured to process the received OFDM symbols and linear distortion byan overlapped Fourier transform function to produce equalized OFDMsymbols. The overlapped Fourier transform function is configured to (i)overlap individual ones of the distorted OFDM symbols with overlappedtime energy from respectively adjacent ones of the distorted OFDMsymbols, (ii) transform the overlapped individual distorted OFDM symbolsinto distorted frequency domain symbols, (iii) perform complexmultiplication of the distorted frequency domain symbols by equalizationcoefficients to equalize the distorted frequency domain symbols, (iv)remove the overlapped time energy from a time domain component of theequalized frequency domain symbols, and (v) produce undistortedfrequency domain symbols from a frequency domain component of the timedomain component with the overlapped time energy removed.

In an embodiment, a digital transmission system includes a transmitterconfigured to transmit (i) a series of orthogonal frequency-divisionmultiplexing (OFDM) symbols having no cyclic prefix attached thereto,and (ii) at least one constant amplitude zero autocorrelation waveformsequence (CAZAC) sequence. The system further includes a receiver forreceiving the transmitted series of OFDM symbols and the CAZAC sequencefrom the transmitter, and a signal path for communicating thetransmitted series of OFDM symbols and CAZAC sequence from thetransmitter to the receiver. The series of OFDM symbols and the CAZACsequence are received by the receiver with linear distortion from thesignal path, and the receiver is configured to utilize the receivedCAZAC sequence as a reference signal for equalizing the received seriesof OFDM symbols.

In an embodiment, a method of equalizing a transmitted digital signalincludes steps of receiving, in the time domain, a sequential series offirst, second, and third data blocks of the transmitted digital signal,forming a compound block in the time domain from the second data blockincluding an end portion of first data block and a leading portion ofthe third data block, performing circular convolution on the compoundblock using a set of equalization coefficients to equalize the compoundblock in the time domain, extracting from the equalized compound block anarrow block corresponding to equalized time domain data of the seconddata block, converting the narrow block from the time domain intofrequency domain data, and reading frequency domain symbols relating tothe second data block from the converted narrow block.

In an embodiment, a method of equalizing a transmitted digital signalincludes steps of receiving, in the time domain, a sequential series oftime domain samples of the transmitted digital signal, forming thereceived sequential series of time domain samples into a separatesub-series of overlapping compound time domain blocks, wherein eachcompound time domain block of the sub-series includes a pseudo-prefixcomprising information from an immediately preceding block, determiningan echo delay on the signal path, converting the compound blocks intothe frequency domain to form compound frequency domain blocks,equalizing the compound frequency domain blocks to form equalizedfrequency domain blocks, converting the equalized frequency domainblocks into the time domain to form equalized time domain compoundblocks, discarding, from the equalized time domain compound blocks,overlapping time domain energy portions corresponding to respectiveequalized pseudo-prefixes, to form narrow equalized blocks, pasting thenarrow equalized blocks together to form a composite equalized timedomain signal, and converting the composite equalized time domain intothe frequency domain and read equalized frequency domain symbolstherefrom.

In an embodiment, a method of modulating a series of input digitalsymbols of a first modulation scheme is provided. The method isimplemented by a transmitter and includes a step of receiving asequential series of samples of the digital symbols in a first domain ofthe first modulation scheme. The first domain is one of the time domainand the frequency domain. The method further includes a step ofdetermining a dual of the first modulation scheme. The dual has a secondmodulation scheme in a second domain that is different from the firstdomain the second domain is the other of the time domain and thefrequency domain. The method further includes steps of applying a 90degree rotational operation to the second modulation scheme to generatea rotational modulation format, modulating the series of digital symbolswith the generated rotational modulation format, and outputting themodulated series of digital symbols to a receiver.

In an embodiment, a digital transmission system includes a transmitterconfigured to transmit an input series of complex symbols, a duobinaryencoder disposed within the transmitter, and configured to filter theinput series of complex symbols and output a partial response signaling(PRS) signal, a converter disposed within the transmitter, andconfigured to convert the PRS signal output into the time domain, and areceiver for receiving the time domain-converted PRS signal from thetransmitter over a signal path.

In an embodiment, a method of modulating an input digital signaltransmission is provided. The method is implemented by a transmitter andincludes steps of receiving the input digital signal having a firsttime-frequency order on the time-frequency axis, rotating thetime-frequency axis by 90 degrees, modulating the input digital signalaccording to the rotated time-frequency axis, and outputting themodulated digital signal to a receiver.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentdisclosure will become better understood when the following detaileddescription is read with reference to the following accompanyingdrawings, in which like characters represent like parts throughout thedrawings.

FIG. 1A is a schematic illustration depicting a conventionaltransmission system.

FIG. 1B is a graphical illustration depicting examples of conventionaltime domain plots for a multiple recursion and a single recursion echoeson a signal path, and respective adaptive equalizer solutionsimplemented to correct the encountered recursion.

FIG. 2A is a graphical illustration of the time domain signal of aconventional OFDM transmission having a cyclic prefix, utilized inaccordance with the example depicted in FIG. 1.

FIG. 2B is a graphical illustration of the frequency domain signal ofthe conventional OFDM transmission depicted in FIG. 2A.

FIG. 3 is a schematic illustration depicting an exemplary multi-carriertransmission system, according to an embodiment.

FIG. 4 is a schematic illustration depicting an exemplary equalizationscheme for an OFDM symbol without a cyclic prefix, utilizing overlappedcircular convolution, in an embodiment.

FIG. 5 is a flow chart diagram of an exemplary circular convolutionprocess for the embodiment depicted in FIG. 4.

FIG. 6A is a schematic illustration depicting an exemplary equalizationscheme utilizing an overlapped Fourier transform, in an alternativeembodiment.

FIG. 6B is a graphical illustration of a histogram depicting adistribution of echo duration for a large population of signal paths.

FIG. 7 is a flow chart diagram of an exemplary overlapped Fouriertransform process for the embodiment depicted in FIG. 6.

FIG. 8 is a graphical illustration of a plot of a transmitted signalhaving in-phase and quadrature components, according to an embodiment.

FIG. 9 is a computer program listing demonstrating an exemplary codingfor implementing the Zadoff Chu sequence depicted in FIG. 8.

FIG. 10 is a graphical illustration depicting a frequency domainspectral plot of the Zadoff Chu sequence depicted in FIG. 8.

FIG. 11 is a flow chart diagram of an exemplary process for simulatingan idealized transmitter-receiver chain for an OFDM transmission havingno cyclic prefix, according to an embodiment.

FIG. 12 is a flow chart diagram of an alternative process for asimulated transmitter-receiver chain for an OFDM transmission having nocyclic prefix, according to an embodiment.

FIG. 13A is a flow diagram depicting an alternative process foroperating the receiver depicted in FIG. 3.

FIG. 13B is a graphical illustration depicting alternative frequencyplots of subcarrier schemes that may be implemented with the processdepicted in FIG. 13A.

FIG. 14 is a graphical illustration depicting a comparative overlay ofan OFDM sinc function implementing a duobinary technique, according toan embodiment.

FIG. 15 is a graphical illustration depicting a comparative overlay of aduobinary OFDM block transmission with a conventional OFDM blocktransmission.

FIG. 16 is a graphical illustration depicting a block time-frequencyplot.

FIG. 17A is a graphical illustration depicting a time domain plot of aduobinary block transmission.

FIG. 17B is a graphical illustration depicting a frequency domain plotof the duobinary block transmission depicted in FIG. 17A.

FIG. 18A is a graphical illustration depicting an impulse response of asingle carrier transmission.

FIG. 18B is a graphical illustration depicting a spectral response ofthe single carrier transmission depicted in FIG. 18A.

FIG. 18C is a graphical illustration depicting an impulse response of aduobinary transmission.

FIG. 18D is a graphical illustration depicting a spectral response ofthe duobinary transmission depicted in FIG. 18C.

FIG. 19A is a graphical illustration of a constellation depictingrelative power calculations for error thresholds of the single carriertransmission depicted in FIGS. 18A-B.

FIG. 19B is a graphical illustration of a constellation depictingrelative power calculations for error thresholds of the duobinarytransmission depicted in FIGS. 18C-D.

FIG. 20 is a graphical illustration depicting a diagram of singlecarrier voltage versus time.

FIG. 21 is a graphical illustration depicting a timing diagram for aspread spectrum signal.

FIG. 22 is a schematic illustration depicting an exemplary block diagramof a system for direct sequence spread transmission and reception.

FIG. 23 is a graphical illustration depicting a received OFDM signal inthe frequency domain.

FIG. 24 is a graphical illustration depicting time and frequencyrelationships between common transmission impairments.

FIG. 25 is a graphical illustration depicting an OFDM modulation matrix.

FIG. 26A is a graphical illustration depicting a Hamming window in thetime domain, according to an embodiment.

FIG. 26B is a graphical illustration depicting an inverse Hammingfunction in the time domain, according to an embodiment.

FIG. 26C is a graphical illustration depicting an implementation of aHamming window on a time domain waveform, according to an embodiment.

FIG. 27A is a graphical illustration depicting a Hamming impulseresponse in the frequency domain, according to an embodiment.

FIG. 27B is a graphical illustration depicting an inverse convolutionimpulse response in the frequency domain, according to an embodiment.

FIG. 28A is a graphical illustration depicting an unequalizedconstellation on which a Hamming window has been implemented.

FIG. 28B is a graphical illustration depicting an equalizedconstellation on which a Hamming window has been implemented.

FIG. 29A is a graphical illustration depicting an implementation of araised cosine voltage function on a time domain waveform, according toan embodiment.

FIG. 29B is a graphical illustration depicting an unequalizedconstellation on which a raised cosine function has been implemented.

FIG. 29C is a graphical illustration depicting a constellation, afterequalization, on which a raised cosine function has been implemented.

Unless otherwise indicated, the drawings provided herein are meant toillustrate features of embodiments of this disclosure. These featuresare believed to be applicable in a wide variety of systems including oneor more embodiments of this disclosure. As such, the drawings are notmeant to include all conventional features known by those of ordinaryskill in the art to be required for the practice of the embodimentsdisclosed herein.

DETAILED DESCRIPTION

In the following specification and the claims, reference will be made toa number of terms, which shall be defined to have the followingmeanings.

The singular forms “a,” “an,” and “the” include plural references unlessthe context clearly dictates otherwise.

“Optional” or “optionally” means that the subsequently described eventor circumstance may or may not occur, and that the description includesinstances where the event occurs and instances where it does not.

Approximating language, as used herein throughout the specification andclaims, may be applied to modify any quantitative representation thatcould permissibly vary without resulting in a change in the basicfunction to which it is related. Accordingly, a value modified by a termor terms, such as “about,” “approximately,” and “substantially,” are notto be limited to the precise value specified. In at least someinstances, the approximating language may correspond to the precision ofan instrument for measuring the value. Here and throughout thespecification and claims, range limitations may be combined and/orinterchanged; such ranges are identified and include all the sub-rangescontained therein unless context or language indicates otherwise.

As used herein, the terms “processor” and “computer” and related terms,e.g., “processing device”, “computing device”, and “controller” are notlimited to just those integrated circuits referred to in the art as acomputer, but broadly refers to a microcontroller, a microcomputer, aprogrammable logic controller (PLC), an application specific integratedcircuit (ASIC), and other programmable circuits, and these terms areused interchangeably herein. In the embodiments described herein, memorymay include, but is not limited to, a computer-readable medium, such asa random access memory (RAM), and a computer-readable non-volatilemedium, such as flash memory. Alternatively, a floppy disk, a compactdisc-read only memory (CD-ROM), a magneto-optical disk (MOD), and/or adigital versatile disc (DVD) may also be used. Also, in the embodimentsdescribed herein, additional input channels may be, but are not limitedto, computer peripherals associated with an operator interface such as amouse and a keyboard. Alternatively, other computer peripherals may alsobe used that may include, for example, but not be limited to, a scanner.Furthermore, in the exemplary embodiment, additional output channels mayinclude, but not be limited to, an operator interface monitor.

Further, as used herein, the terms “software” and “firmware” areinterchangeable, and include any computer program storage in memory forexecution by personal computers, workstations, clients, and servers.

As used herein, the term “non-transitory computer-readable media” isintended to be representative of any tangible computer-based deviceimplemented in any method or technology for short-term and long-termstorage of information, such as, computer-readable instructions, datastructures, program modules and sub-modules, or other data in anydevice. Therefore, the methods described herein may be encoded asexecutable instructions embodied in a tangible, non-transitory, computerreadable medium, including, without limitation, a storage device and amemory device. Such instructions, when executed by a processor, causethe processor to perform at least a portion of the methods describedherein. Moreover, as used herein, the term “non-transitorycomputer-readable media” includes all tangible, computer-readable media,including, without limitation, non-transitory computer storage devices,including, without limitation, volatile and nonvolatile media, andremovable and non-removable media such as a firmware, physical andvirtual storage, CD-ROMs, DVDs, and any other digital source such as anetwork or the Internet, as well as yet to be developed digital means,with the sole exception being a transitory, propagating signal.

Furthermore, as used herein, the term “real-time” refers to at least oneof the time of occurrence of the associated events, the time ofmeasurement and collection of predetermined data, the time for acomputing device (e.g., a processor) to process the data, and the timeof a system response to the events and the environment. In theembodiments described herein, these activities and events occursubstantially instantaneously.

As described herein, signal equalization in the time domain may beperformed at a receiver by capturing symbols of the received symbol intoan overlapped compound block and circularly convolving the compoundblock with an inverse channel response to produce an equalized compoundblock. End portions of the equalized compound block may then bediscarded to produce a narrow equalized block, and a plurality of suchnarrow equalized blocks may further then be cascaded to form ade-ghosted signal stream. Alternatively, the overlapped compound blockmay be processed in the frequency domain using frequency domainequalization. In an exemplary embodiment, cyclic prefixes are not senton OFDM or OFDMA multicarrier transmissions. In alternative embodiments,the present techniques may be implemented on any type of linearlydistorted modulation transmission without a cyclic prefix (also known asguard intervals or cyclic extensions), or transmissions using relativelyshort cyclic prefixes.

In the exemplary embodiment, systems and methods herein are configuredto transmit OFDM and OFDMA signals through wired and wireless channelswithout considering, or having to create, cyclic prefixes. In someembodiments, overlapped circular convolutions are performed at thereceiver end of the system to eliminate linear distortion, such asechoes. In such embodiments, the overlapped circular convolution may beprogrammed with equalization coefficients obtained, for example, frompilot subcarriers or from a training-synchronization signal, such as aconstant amplitude zero autocorrelation (CAZAC) signal. Each receivedfrequency coefficient may then be corrected by a single complexmultiplication to correct the respective magnitude and phase. In atleast one embodiment, a Zadoff Chu sequence functions as thetraining-synchronization signal.

In other embodiments, overlapped Fourier transforms and inverse Fouriertransforms are performed at distinct signal conversion stages, and thepseudo-prefixes are determined at the receiver end of the systemaccording to predetermined pilot/training signals, or from other signalenergy received from the transmitter. For example, irrespective ofwhether a transmitter creates a new cyclic prefix to serve as a guardinterval between transmitted data, the present systems and methodsutilize the receiver to determine a pseudo-prefix from random ornoise-like portions of the transmission (by performing anautocorrelation), or from training signals, or pilots. Therefore, thepresent systems and methods are equally effective for receiving digitaltransmissions that include, or do not include, cyclic prefixes from thetransmitter. Accordingly, by eliminating (or ignoring) the need forcyclic prefixes, the bandwidth efficiency of transmissions may beincreased to allow a frequency band to transport more data within atime-frequency resource, and thereby reduce power consumption andincrease the battery life of system components.

The embodiments herein are of also of particular use with respect toOFDM signals, which are sent in blocks, and include a number ofharmonics that are orthogonal to each other because of their integerrelationship to a fundamental frequency. By varying the phase and themagnitude of the harmonics, information can be transmitted whilepreserving the orthogonality between each of the harmonics. As describedin greater detail below, echoes may affect OFDM signals, but can becorrected in the frequency domain. Conventional systems only correct forthe effects of inter-block distortion by using a time domain cyclicprefix. Correction schemes using cyclic prefixes, however, are onlyfully effective if the delay of the echo is shorter than the duration ofthe cyclic prefix/guard interval. In multi-carrier transmission schemesthough, the length of echo delay can vary from receiver to receiver, oraccording to the respective distances from reflection points in a signalpath. The present embodiments address and solve this multicarrier echovariance problem by pseudo-prefix determination at the receiver end.

As described herein, transmission efficiency is increased by eliminatingthe cyclic prefix from transmitted OFDM or OFDMA blocks. Alternatively,reception efficiency may also be increased by configuring the receiversuch that the cyclic prefix may be disregarded, if a CP is included in adigital transmission from the transmitter. In an exemplary embodiment,equalization is accomplished in the time domain through use of anoverlapped circular convolution process, which overlaps a selected blockwith surrounding information to form a larger compound, or “fat,” block.The compound block is then circularly-convolved with programmed timedomain coefficients to remove distortion, and thus equalize the compoundblock. After equalization, the compound block is “trimmed” into anequalized narrow block, which is then converted into the frequencydomain. OFDM symbols may then be determined from the equalized, narrow,converted frequency domain block.

In an alternative embodiment, the cyclic prefix is eliminated in thefrequency domain through use of an overlapped Fourier transform. In thisalternative process, a large compound time domain block of an OFDMcarrier is transformed into the frequency domain, and then equalized bycomplex multiplication FDE sub-process. This equalized compoundfrequency domain block is transformed back into the time domain, andthen trimmed to form an equalized, time domain, narrow block. In anexemplary embodiment, because the original signal is an OFDMtransmission, and additional Fourier transform (e.g., an FFT) isperformed on the narrow block so that the OFDM symbols may bedetermined.

Use of cyclic prefixes is known in the art to provide more than onlyblock-to-block isolation. For example, if a received signal iscross-correlated with a delayed copy of itself, a phase shift on aresulting correlation peak will reveal any offset frequency between thetransmitter and the receiver, and correction may then be applied.However, as described further below, this additional functionality fromthe cyclic prefix is advantageously replaced by a constant amplitudezero autocorrelation (CAZAC) function signal, such as a Zadoff Chusequence. In some embodiments, the Zadoff Chu sequence is implementedtogether with channel characterization for further equalizationpurposes, as well as block timing information.

Overlapped Circular Convolution

FIG. 3 is a schematic illustration depicting an exemplary multi-carriertransmission system 300. System 300 includes a first transmitter 302having a first transmitting antenna 304 and a second transmitter 306having a second antenna 308. First and second transmitters 302, 306transmit first and second carrier signals 310, 312, respectively, overcommunication channels 314 to a first receiver 316 and a second receiver318. In the example shown in FIG. 3, two receivers and two transmittersare illustrated for simplicity of explanation. In operation, many moretransmitters and/or receivers may be implemented within system 300.

Alternatively, the embodiments described herein advantageously operatein the case where multiple receivers are receptive to different carriersignals from multiple transmitters and also in the case where a multipletransmitters deliver a number of different carrier signals to aplurality of antennas (e.g., multiple-input/multiple-output (MIMO).Accordingly, communication channel 314 may include wired signal paths,wireless signal paths, or combination of both. In the example shown inFIG. 3, first receiver 316 receives a composite signal 320. In at leastsome embodiments, composite signal 320 further includes at least oneecho 322 of first carrier signal 310(1), reflected off of a reflectingobject 324. For ease of explanation, potential reflections of firstcarrier signal 310(2) and second carrier signal 312 are not shown.

FIG. 4 is a schematic illustration depicting an exemplary equalizationscheme 400 for equalizing an OFDM symbol without a cyclic prefix,utilizing overlapped circular convolution. In an exemplary embodiment,equalization scheme 400 is implemented by a receiver or a processorthereof (e.g., first receiver 316, FIG. 3), and equalization isperformed in the time domain. A received time domain OFDM carrier signal402 includes a series of time domain blocks 404, 406, 408, which arelabeled herein as “W” block 404, “X” block 406, “Y” block 408,respectively. Each of W block 404, X block 406, and Y block 408 containspotential distortion, and includes OFDM data symbols, but no cyclicprefixes. For ease of explanation, only three blocks are shown in thisexample; however, OFDM carrier signal 402 may include significantly moreblocks in the series, or be continuous in the time domain.

In operation, the receiver/processor selects X block 406, and forms acompound block 410, which includes all of X block 406, an end portion412 of W block 404, and a beginning portion 414 of Y block 408. In thisexample, end portion 412 and beginning portion 414 are illustrated to beone fraction (k) of W block 404 and a different fraction (m) of Y block408, respectively. Nevertheless, a person of ordinary skill in the artwill understand that end portion 412 and beginning portion 414 mayconstitute larger or smaller portions of the respective origin blocks,equal portions, or portions of unequal length. End portion 412 thusfunctions as a pseudo-prefix, in the time domain, for X block 406.Pseudo-prefixes function differently from conventional cyclic prefixes.Whereas a conventional cyclic prefix for X block 406 would require arepetition of information from the trailing portion of the X blockitself, the present pseudo-prefix is based on information from thepreceding W block 404, and therefore requires no repetitive data. In asimilar manner, beginning portion 414 of the following Y block 408functions as a “pseudo-suffix” in the time domain for X block 406.Pseudo-prefixes and pseudo-suffixes are generally referred to herein as“pseudo-extensions.” In this example, blocks W, X, and Y are all subjectto a same linear distortion.

In further operation, compound block 410 is convolved with equalizationcoefficients 416 (eight coefficients, C0-C7, are illustrated; howevermuch larger numbers of coefficients, e.g., 64 or more, may be processedaccording to this embodiment) to form an equalized convolution block418, which remains in the time domain. That is, each term in compoundblock 410 is multiplied by the respective coefficient 416 determinebeneath it, and the products are summed. A circular shift (to the right,as illustrated in FIG. 4) of the top row (i.e., compound block 410) isperformed, in the process is repeated until the circular convolution iscomplete. Data from equalized convolution block 418 is subjected to oneor more circular convolutions. Nevertheless, the size of equalizedconvolution block 418 remains the same before and after the circularconvolution process(es). After circular convolution, symbols from endportion 412 and beginning portion 414 (associated with W block 404 and Yblock 408, respectively) are trimmed from equalized convolution block418 to form a narrow equalized block 420, or X′ block 420, whichrepresents a de-ghosted version of X block 406. That is, the time domainpseudo-prefix and pseudo-suffix information is removed, and X′ block 420may then be converted into the frequency domain, after which the OFDMsymbols may be determined (step not illustrated).

In an exemplary embodiment, equalization scheme 400 is implementedsequentially for each of the series of distorted time domain blocks 404,406, 408. That is, after the formation of X′ block 418, equalizationscheme 400 similarly forms a compound block (not shown) from Y block 408(e.g., using portions from preceding X block 406 and a following (Z)block, also not shown), and performs circular convolution thereupon tocreate an equalized Y′ block (not shown) nominally using the samecoefficients. In an alternative embodiment, equalization scheme 400 maybe performed on individual blocks of OFDM carrier signal 402non-sequentially, that is, Y block 408 may be equalized before W block404. In at least one embodiment, some blocks of OFDM carrier signal 402may be equalized, while equalization is not performed other blocksaccording to equalization scheme 400. Conventional (non-overlapped)multi-carrier technology of OFDM encounters problems in theimplementation of circular convolutions, in that extraneous energy fromone block contaminates adjacent blocks. According to the embodimentsdescribed herein, this inter-symbol interference is eliminated.

According to equalization scheme 400, which uses an overlapped circularconvolution, linear distortion may be removed from any received signalin the time domain irrespective of whether the received signal containsa CP, and irrespective of the underlying modulation used. The receivedsignal may be viewable in the time domain (e.g., single-carrier orSC-FDMA), or in the frequency domain (e.g., OFDM and OFDMA),spread-spectrum or wavelet based. In some embodiments, pseudo-extensions412, 414 may be or include quiet time, another type of signal sufferingthe same linear distortion, an unused cyclic prefix, or a trainingsignal. The signal may even be a baseband, such as an audio signalhaving an echo. In the exemplary embodiment, the pseudo-extensions arelonger than the relevant encountered echo and all recursions in the echosolution. That is, the respective pseudo-prefix is longer than thetrailing echo(es), and the respective pseudo-suffix is longer than theleading echo(es) plus recursions.

FIG. 5 is a flow chart diagram of an exemplary circular convolutionprocess 500 for equalization scheme 400, FIG. 4. In the exemplaryembodiment, process 500 is implemented by a receiver or the processorthereof (e.g., first receiver 316, FIG. 3), and the equalizationsimilarly occurs in the time domain with an overlapped circularconvolution. Process 500 begins at step 502, in which a digitaltransmission signal (e.g., OFDM carrier signal 402, FIG. 4) is received,including a series of sequential OFDM W, X, Y blocks (e.g., time domainblocks 404, 406, 408, FIG. 4). In step 504, a compound block (e.g.,compound block 410, FIG. 4) is created from the entirety of the X block,an end portion of the W block, and the beginning/lead portion of the Yblock. In step 506, circular convolution is performed on the compoundblock and its respective coefficients (e.g., coefficients 416, FIG. 4).In step 508, an equalized narrow block (e.g., narrow block 418, FIG. 4)is extracted from the compound block by trimming/discarding the W(pseudo-prefix) and Y (pseudo-suffix) portions of the convolved compoundblock. In step 510, the equalized narrow block is converted into thefrequency domain (e.g., by an FFT), and the OFDM symbols are read fromthe frequency-converted narrow block. In step 512, steps 502 through 510are optionally repeated for the next block in the sequence. That is, instep 512, a compound block is formed from the entirety of the Y block,together with portions of the unequalized X block and “Z” block, tocreate an equalized Y′ block. Alternatively, in step 512, a distortedblock other than the Y block may be equalized. If step 510 is optionallyeliminated, and the signal being received is single-carrier, the narrowblock will contain the equalized time domain symbols.

The present embodiments thus overcome the known problems associated withthe use of cyclic prefixes, described above. By implementing the presentprocessing techniques at the receiver end, a digital signal transmissionsystem is able to overcome failures that would occur in a multi-carrierscenario when a cyclic prefix is too short, that is, has a shorterduration than an echo/reflection in the time domain. When the cyclicprefix is too short, the conventional receiver may fail. In contrast, byimplementing a pseudo-prefix that is adjustable in time and adjustableaccording to echo duration, the receiver according to the presentsystems and methods will continue to function irrespective of thelength—or existence—of the cyclic prefix.

Overlapped Fourier Transform

FIG. 6A is a schematic illustration depicting an alternativeequalization scheme 600 utilizing an overlapped Fourier transform.Similar to equalization scheme 400, FIG. 4, equalization scheme 600 maybe implemented in accordance with system 300, FIG. 3, and eliminates theneed for cyclic prefixes, implementing frequency domain equalization forcomputational efficiency on large transforms.

In operation, a receiver (e.g., first receiver 316, FIG. 3) of scheme600 receives a series of OFDM symbols 602 displayed in the time domain.As described above, in conventional OFDM transmission, the energytransportation problem between blocks of data, also known as inter-blockinterference (IBI) or “leakage,” is addressed by the use of cyclicprefixes. In single-carrier optical implementations, overlap frequencydomain equalization (OFDE) has been proposed to eliminate the cyclicprefixes. However, such single-carrier OFDE implementations have notaccounted for the variable length of echoes, and particularly the typeof echo variability and dispersion that can occur in a multi-carriersystem. The conventional OFDE techniques set arbitrary values to theamount of time domain overlap (CP length) based on anticipated chromaticdispersion, and thus may not obtain leakage-free transforms because theecho may be longer than anticipated. Echo energy, for example, maypersist longer than the discarded portion 412.

In contrast to these conventional techniques, scheme 600 forms acompound block 604 from OFDM time domain symbols 602 such that compoundblock 604 is of sufficient size to allow an encountered echo (plussignificant recursions, if any) to die out within portions of compoundblock 604 that may be subsequently discarded after equalization has beenperformed. Specifically, each compound block 604 of time domaininformation includes a data portion 606, a pseudo-prefix portion 608,and a pseudo-suffix portion 610. In the exemplary embodiment, therespective sizes of extension portions 608, 610 may be determinedindependently from the size of data portion 606. Where cyclic prefixesare utilized, the conventional system is required to optimize thetrade-off between the package size of the data portion and the amount ofthe transmission utilized to include the cyclic prefix. According to thepresent system, on the other hand, this trade-off is eliminated. Thepseudo-extensions may be set to any length that is needed to address anencountered echo. The pseudo-extensions may utilize portions, or theentirety, of the data portions of adjacent blocks, and may even includedata from more than one adjacent block if such length is necessary.

Furthermore, the size/duration of pseudo-prefix portion 608 may bedetermined independently from the size of pseudo-suffix portion 610.That is, in some cases, a trailing echo might be of a significantlydifferent duration than a leading echo. A receiver configured accordingto the present embodiment is thus advantageously configured to becapable of dynamically adjusting each extension portion 608, 610according to the actual echoes encountered in real time for therespective data portion 606. Extension portions 608 and 610 thus formthe overlapping regions of the compound block and, although theseportions are not themselves cyclic prefixes, these overlapping portionsare further capable of advantageously performing the same functionalguard purpose as the cyclic prefix, but without requiring additionaltransmission time. The overlapping portions 608, 610 represent anextension period of time for echoes to die out that need not becyclic/cyclical.

In further operation, after OFDM time domain symbols 602 have beenformed into compound blocks 604, compound blocks 604 are converted intothe frequency domain (e.g., by an FFT), to form compound frequencydomain blocks 612, upon which frequency domain equalization (FDE) isthen performed, for example, using a complex multiplication on eachsubcarrier with an inverse channel coefficient. Equalized compoundfrequency domain blocks 612 are then transformed back into the timedomain (e.g., by an IFFT) to form equalized compound time domain blocks614. Each equalized compound time domain block 614 includes equalizeddata 616, an equalized pseudo-prefix 618, and an equalized pseudo-suffix620. The respective equalized pseudo-prefixes 618 and equalizedpseudo-suffixes 620 are cut from the equalized compound time domainblocks 614 to extract equalized data 616. Blocks of equalized data 616may then be pasted together to form a single equalized time domainsignal 622, if desired.

The single equalized time domain signal 622 may then be transformed intothe frequency domain to form a composite stream of equalized OFDM data,constituted of individual OFDM blocks 624, 626, and 628. That is, thefrequency domain composite stream is made up of individual frequencydomain blocks (e.g., block 624), which each correspond with a respectivedata portion (e.g., portion 606). In an exemplary embodiment, individualfrequency domain blocks 624, 626, and 628 are pasted together as onesequenced composite block. In an alternative embodiment, each individualfrequency domain block 624, 626, 628, etc. is processed separately todetermine OFDM signals therefrom. In the exemplary embodiment,equalization scheme 600 considers each compound block 604 in the orderof transmission, and thus repeats the process on an ongoing overlappedbasis for each following block of the received OFDM time domain signals.

In some embodiments, data portion 606 is anchored according to thecenter time of the frequency duration equalization signal (e.g., blocks612), and a de-ghosted time domain signal (e.g., equalized time domainsignal 622) is formed by combining the equalized-and-transformed odd andeven time domain blocks corresponding to data window portions 606. Thatis, after frequency domain equalization, the trimmed odd and even blocksof equalized data can be put back together to form an equalized timedomain signal. For single carrier, such as pulse amplitude modulation(PAM) signals, the final time domain symbol sequence is considered“clean,” and may then be subject to “slicing” and forward errorcorrection (FEC). For OFDM symbols, the final equalized time domainsymbol sequence is converted into the frequency domain before slicingand optionally implementing FEC. In DOCSIS implementations, eliminationof the cyclic prefix allows for faster data transfer, which would beapproximately a 15% improvement for a symbol period of 20 μs and acyclic prefix of 3 μs.

The techniques described herein may additionally be implemented by thereceiver irrespective of what type of signal is, or signals are,received from the transmitter(s). The pseudo-prefixes andpseudo-suffixes are made sufficiently long relative to the duration ofthe longest echo, and its recursions, and thus the linear distortionfrom the echo(es) can be completely removed. As described above, becauseleading and trailing echoes are not necessarily of equal length, thepresent embodiments realize the additional advantage of allowing thereceiver to dynamically adjust the pseudo-prefix independently of thepseudo-suffix to address the actual distortion encountered, and withoutsacrificing the size of the data package. In some embodiments, anoptional windowing function, such as a raised cosine window, may beplaced on pseudo-prefix portion 608 and/or pseudo-suffix portion 610prior to performing FDE.

In at least one embodiment, the size of the pseudo-extensions may be setto a predetermined threshold value that represents a duration of thelongest echo expected to be encountered among a system includingmultiple transmissions from different transmitters (OFDMA). The echo maybe determined, for example, from the channel response associated withthe respective signal path. In an alternative embodiment, the size ofone or more pseudo-extension is set to be greater than a size necessaryto remove the distortion from an echo dynamically measured along thepath by the receiver during signal characterization. In a furtheralternative embodiment, the receiver is configured to implementpseudo-extensions of sufficient size to eliminate the distortion fromexpected echoes on the signal path, and also measure the transmittedsignals and dynamically adjust the predetermined size of thepseudo-extensions when encountering an echo having an unexpected lengthgreater than the predetermined threshold.

In at least one embodiment, a frequency domain equalizer is programmedto utilize pilot signals for training prior to frequency domainequalization. In this embodiment, magnitude and phase correction arecalculated to render the pilot signals sufficient for use. In oneexample, continuous pilots are used for synchronization, and timing forthe start of a block may be determined by subjecting a set of capturedpilots to an IFFT, with a zero value inserted for all data subcarriers,and a resulting time domain impulse response will indicate early or latetiming. In at least one alternative embodiment, the time domain signalequalizer is programmed blindly, or using conventional training signalsprior to frequency domain equalization. Interpolation of channelresponse between subcarrier pilots may be used, provided that the pilotspacing is closer than a predetermined minimum value. When the echoduration is longer, for example, the frequency domain ripple will have ashorter period, and should therefore implement closer pilot spacing. Insome embodiments, as explained further below in greater detail, cyclicprefixes, pilot signals, and training signals may be completelyeliminated through a novel use of constant amplitude zeroautocorrelation (CAZAC) function. In the exemplary embodiment, thechannel response is determined prior to slicing and FEC. The finalequalized and trimmed frequency domain blocks back together to determinethe OFDM symbols need not be pasted together (e.g., element 622).

FIG. 6B is a graphical illustration of a histogram 630 depicting adistribution of echo duration for an increasing population of receivers.More particularly, histogram 630 illustrates, for a large population ofreceivers, the considerations that must be addressed for echoes ofincreasing time delays for the receivers to sufficiently function. Thedistribution curve of histogram 630 might be encountered, for example,in a broadcast signal distribution network, or in the case where a largenumber of receivers are disposed within a relatively small geographicdistance from one another (e.g., a large number of mobile telephonesbrought into a football stadium or public event). Histogram 630 depictsa first echo time interval 632, a second echo time interval 634, and athird echo time interval 636.

First time interval 632 represents a time delay that could be addressedby a typical conventional cyclic prefix. Second time interval 634represents the duration of a time delay that could be addressed by acyclic prefix having a compromise value of increased duration accordingto the trade-off optimization discussed above. The length of thecompromise cyclic prefix might be increased, but at the sacrifice of thesize of payload data and the transmission. Beyond the length of secondtime interval 634, the trade-off between the payload and the guardinterval is too great to make further increases in the guard intervalpractical. Second time interval 634 thus represents the maximum timedelay that a conventional system is capable of addressing utilizing acyclic prefix. Third time interval 636 therefore represents theworst-case echo delay that a system is likely to encounter for receiversin the network, and which require equalization for all of the receiversto properly function. A significant percentage of receivers in thenetwork (represented by hashed area 638 in FIG. 6B) will encounterechoes beyond the maximum capability, i.e. compromise interval length634, of the conventional system, and will therefore experienceequalization difficulties.

Systems and methods according to the present embodiments though, arecapable of fully equalizing all of the receivers in the network, andwithout requiring any consideration of the cyclic prefix length, or thetrade-off of the cyclic prefix length against length of the datapackage. That is, in the conventional system, if a transmitted cyclicprefix is made to sufficiently long enough to equalize the longest echothat can be encountered in the network, the size of the transmittedpayload will be too small to make the transmission efficient. As thelength of the cyclic prefix is shortened for better transmissionefficiency, the number of receivers that will encounter equalizationproblems increases. Conventional OFDM/OFDMA systems therefore arerequired to strike a balance between the number of reception sites andpoor transmission efficiency. According to the present systems andmethods, on the other hand, this balance may be completely ignored.Although the pseudo-extensions of the present embodiments may performthe functions of cyclic prefixes, the pseudo-extensions are not bound byany of the cyclic prefix limitations. The pseudo-extensions aredetermined independently from the payload/data package, and may evenutilize adjacent blocks of payload data as the pseudo-extensions (butdiscarded after equalization of the desired block).

Some conventional systems have been proposed to eliminate cyclicprefixes from single carrier optical transmissions. These single carrierproposals, however, are unable to cope with channels that fade to zero.That is, division by zero cannot be performed where channel response iszero. In wireless channels, signals from multiple antennas can becombined to produce a composite signal without frequency response nulls.That is because, it two antennas are spaced apart, it is very unlikelythat a complete fade will occur at a same frequency for both antennas.Moreover, conventional techniques of eliminating cyclic prefixes onlybeen proposed for single carrier transmissions exhibiting chromaticdispersion on fiber optic lines. Fiber optics, however, do not typicallyencounter discrete echoes, as described above. Furthermore, OFDMtransmission is multi-carrier, and may be implemented on both wired andwireless networks, where echoes may be commonly encountered.

FIG. 7 is a flow chart diagram of an exemplary overlapped Fouriertransform process 700 for equalization scheme 600, FIG. 6A. In theexemplary embodiment, process 700 is implemented by a receiver or theprocessor thereof (e.g., first receiver 316, FIG. 3). Process 700 beginsat step 702, in which a digital transmission signal (e.g., OFDM carriersignal 602, FIG. 6) is received, including a series sequential OFDM timedomain samples, and formed into overlapping series of compound timedomain blocks (e.g., blocks 604, FIG. 6A). In some embodiments, process700 is particularly useful if the received time domain symbols are froma single carrier transmission, or from a direct sequence spread spectrumtransmission. In an optional embodiment, the narrow blocks, such as dataportions 606, are centered in the respective compound block 604, and areof sufficient size to allow echoes to die out (e.g., go to zero) inbetween bursts.

In step 704, the compound time domain blocks are converted into thefrequency domain (e.g., by an FFT). In step 706, the frequency domainblocks are equalized using frequency domain equalization. In step 708,the equalized compound frequency domain blocks are converted into thetime domain (e.g., by an IFFT) to create equalized compound time domainblocks (e.g., blocks 614, FIG. 6). In step 710, the “early” (e.g.,pseudo-prefix 618, FIG. 6A) and “late” (e.g., pseudo-suffix 620, FIG.6A) time symbol ends are cut/discarded from the equalized compound timedomain blocks to extract narrow equalized time domain blocks (e.g.,blocks 616, FIG. 6).

Step 712 is a decision step. In step 712, a processor of the receiverdetermines whether received input symbols are single carrier ormulticarrier (OFDM). If the received time domain symbols are determinedto be single carrier, process 700 proceeds to step 714, where the narrowequalized time domain blocks are pasted together to form an equalizedtime domain signal (e.g., signal 622, FIG. 6) and, for single carriersignals (or the equivalent) then sliced and forward error corrected. Inat least one example of step 714, where the input symbols are, forexample, a direct sequence spread spectrum (not shown), step 714 furtherincludes an optional sub-step of de-spreading the symbols. If, however,in step 712, the processor of the receiver determines that the inputsignals are multicarrier signals (e.g., OFDM/OFDMA), process 700proceeds to step 716, where the equalized time domain signal isconverted into the frequency domain, after which slicing/FEC may beimplemented, and/or OFDM symbols are read therefrom. In someembodiments, narrow blocks may include multiple OFDM transforms, whichare separated prior to performing the FFT of step 716. In otherembodiments, the narrow blocks may alternatively or additionally includepartial OFDM transforms, which are combined to perform the FFT of step716.

In an alternative embodiment, process 700 further includes optional step718. Step 718 is implemented in the case where compound time domainblocks form a continuous stream, as opposed to burst mode reception. Insuch cases, optional step 718 proceeds to the next block in sequentialtime order and repeats process 700 for the next block. According toprocess 700, frequency domain equalization can be performed on multipleblocks the same time, and across block boundaries. Alternatively, oradditionally, a large block can also be broken into smaller sub-blocksfor separate equalization.

According to this advantageous process, a receiver may be configured orprogrammed to dynamically adjust the size of the compound blockaccording to the length of an encountered echo on the signal path. Forexample, if a very long echo is encountered in the signal path, the sizeof the overlapping compound blocks can be enlarged at the receiver endto effectively create longer pseudo-prefixes having a greater durationthan the encountered echo. Such dynamic adjustability is particularlyadvantageous with respect to terrestrial broadcast signals, which areknown to suffer from very long echoes in the signal path. Theequalization processes described herein are thus effectivelymodulation-indifferent to the type of data that is being linearized, andthus is fully and simultaneously adaptable to single carrier,multi-carrier, or spread spectrum transmissions. According to theembodiments herein, the data may be continuous, or formed intoindividual blocks.

Similarly, the size of the transform block may also be dynamically madelarger or smaller as desired, and each separate path may be converted bythe transform of a different size than that implemented on a differentpath. This ability to dynamically alter the transform size provides areceiver with superior versatility over conventional OFDE techniques,which implement a one-size-fits-all transform approach. In conventionalOFDM transmissions, for example, FFT length is made large in order toprevent the overhead of the cyclic prefix from becoming too burdensomeas a percentage of the total transmission time. However, phase noisebecomes more unstable as the length of the transform increases. Thepresent embodiments address this problem by both (i) rendering thetransform size dynamically adjustable, and (ii) eliminating the need forcyclic prefix transmission at the transmitter end.

Zadoff-Chu Sequence as a Pseudo-Prefix

FIG. 8 is a graphical illustration of a plot 800 of an exemplarytransmitted signal 802 having in-phase (I) components 804 (black) andquadrature (Q) components 806 (gray). Signal 802 may be used, forexample, as a demonstration signal. Plot 800 depicts linear voltage overtime of captured signal 802. The I and Q components are also sometimesreferred to as the real and imaginary samples, respectively, andorthogonal to one another. In this example, plot 800 is obtained from atest system using a software-defined radio (SDR, not shown) as atransmitter, which is an Ettus (National Instruments) model B200.Another B200 SDR is used as a receiver (also not shown), which willintroduce frequency error due to the different oscillators of the SDRs.The test system receiver captures at 8 million samples per second (i.e.,an 8 MHz channel), and transmitted signal 802 includes a group of 15contiguous OFDM blocks 812, each 64 symbols wide (i.e., subcarrierspacing of 125 kHz). In the example illustrated in FIG. 8, testing wasperformed at a center frequency of 840 MHz and 2.4 GHz, with bandwidthsof both 8 MHz and 16 MHz.

In the test system this example, transmitted signal 802 further includesa first CAZAC function 808 and a second CAZAC function 810. Asillustrated in FIG. 8, first and second CAZAC functions 808, 810 areZadoff Chu sequences placed on either end of the 15 OFDM data sequences812 therebetween. A Zadoff Chu sequence is a particular type of CAZACfunction that has no crest factor, and operates as a constant envelopetime domain waveform. In operation, the Zadoff Chu sequence waveforms808, 810 are captured from the antenna periodically from transmittedsignal 802, which then allow the determination of the offset frequency,the start of the OFDM block, and the channel characterization.

More particularly, the Zadoff Chu sequences 808, 810 operate as async/timing signal to establish an exact offset frequency differencebetween the transmitter and receiver by a time domain cross-correlationprocess. Cross-correlation provides exact timing and establishes theprecise start of each of the 15 OFDM blocks 808. Accordingly, the useand placement of the Zadoff Chu sequences 808, 810 serves a threefoldfunction: (i) offset frequency measurement; (ii) start of blockdetection; and (iii) channel response determination for equalizationcoefficients.

In operation, plot 800 is representative of either a wireless or wiredtransmission, and measurement of the frequency differences between thetransmitter and the receiver carriers is performed by cross-correlatingthe time domain Zadoff Chu sequences 808, 810 to produce across-correlation with real and imaginary components measured at peakvalues. Accordingly, a time domain phase error between Zadoff Chusequences 808, 810 is the arctangent of the imaginary value divided bythe real value. Frequency error may then be eliminated by de-rotatingthe captured complex samples, and then the OFDM block group 812 may beparsed to create 15 complex time domain blocks, which, as described withrespect to the embodiments above, may include the selected OFDM block,part of a previous OFDM block, and part of the subsequent OFDM block. Asalso described above, such portions of the previous and subsequentblocks may include other OFDM data signals themselves, all or part ofthe Zadoff Chu sequences 808, 810, or no energy (quiet time) etc. In analternative embodiment, data sequences 812 include one or more of singlecarrier blocks, dead-air (quiet) time, direct-sequence spread spectrum,or any other type of mixed signals experiencing the same lineardistortion. That is, linear distortion can be removed from any signaltransmitted in the block allocated to data sequences 812.

Similar to the processes described above (see e.g. FIGS. 6-7), all 15 ofthe compound time domain blocks may then be further converted into thefrequency domain, equalized, converted back into the time domain,trimmed to become narrow, equalized, time domain blocks, and finally(e.g., for OFDM signals, as described above) converted into thefrequency domain where the component OFDM symbols may be determined.This example, frequency domain equalization coefficients may bedetermined by performing a Fourier transform/FFT on first Zadoff Chusequence 808, and then performing a complex division by a stored complexcoefficient for each symbol (in frequency). In some embodiments, thecompound blocks will require more coefficients than the particularfrequency domain equalization coefficients provided in the Zadoff Chusequence (64 in this example), and therefore the equalization solutionis interpolated to create at least twice the number (e.g., 128) offrequency domain coefficients.

In an exemplary embodiment, the combination of the Zadoff Chu sequence808 and OFDM block group 812 forms a trained block group (not separatelynumbered). In this example, a continuous transmission may therefore becreated by transmitting a series of such trained block groups.Alternatively, a burst mode transmission may be created by transmittinga single trained block group, followed by a single ZC sequence forfrequency offset estimation. In at least one embodiment, a plurality ofquiet time symbols (e.g., 8 symbols) are placed on either side of bothZadoff Chu sequences 810, 812, to further prevent energy from some datasymbols contaminating the channel characterization results.

In at least some embodiments, because an initial Zadoff Chu sequence(e.g., sequence 808) is effectively repeated (e.g., sequence 810) for asingle block of OFDM signals, the CAZAC functions/Zadoff Chu sequencesaccording to plot 800 may perform further advantageous utility as asubstitute for cyclic prefix, or pseudo-prefix, for transmissionimplementations that still intend to utilize cyclic prefixes. That is,the Zadoff Chu sequence may be utilized as a substitute cyclic prefix(because it is repeated energy), in addition to the functionalitydescribed above, namely, offset frequency measurement, block startdetection, and use as a training signal. Accordingly, implementation ofthe present Zadoff Chu sequence techniques allows for not only thesubstitution for other types of transmissions, but also for theimprovement of OFDM transmissions that still desire to utilize cyclicprefixes.

Therefore, cyclic prefix elimination provides greater data throughput tothe transmission system as a whole, and the utilization of the ZadoffChu sequences instead of the cyclic prefixes provides a more accurateoffset frequency estimation. Additionally, utilization of thehigh-energy, no crest factor Zadoff Chu sequences instead of pilotsignals provides a cleaner, less noisy channel model. Accordingly,systems and methods according to the present embodiments realizesignificantly improved performance over conventional OFDM transmissionschemes that utilize cyclic prefixes and/or pilots, because the ZadoffChu sequence has a zero dB crest factor (as compared with the 10-16 dBfactor of OFDM), and therefore allows a stronger signal that can be usedfor timing, characterization, and frequency offset, thereby resulting inlonger battery life, greater range, and greater throughput of systemreceivers, which is particularly important for portable handheld devices(e g, cellular phones, tablets, portable computers, etc.). Moreover,elimination of the cyclic prefix is of particular importance at thetransmitter and as well, because it will result in significant powersavings, thereby delaying the need for plant upgrades, while allowingfor improved service tiers.

FIG. 9 is a computer program listing 900 demonstrating an exemplarycoding for implementing the Zadoff Chu sequence depicted in FIG. 8.According to listing 900, a computer code generates 63 complex ZadoffChu values. A 64^(th) Zadoff Chu point is created by repeating the63^(rd) Zadoff Chu value. Accordingly, a radix 2 FFT operation may beimplemented as listed. The person of ordinary skill in the art willunderstand though, that in FFT operation may be implemented for otherbase values, or prime numbers, without departing from the scope of theembodiments described. In an exemplary embodiment, computer programlisting 900 is based on a C code programming language, but otherprogramming languages, including Matlab may also or alternatively beused.

The Zadoff Chu sequences herein represent complex-valued mathematicalsequences which, when applied to radio signals, give rise to anelectromagnetic signal of constant amplitude. Cyclically shiftedversions of the Zadoff Chu sequence, imposed on a transmitted signal,thereby result in zero correlation with one another at the receiver. Agenerated Zadoff Chu sequence that has not been shifted is referred toas a “root sequence”.

The Zadoff Chu sequences described herein exhibit a further usefulproperty namely, that cyclically-shifted versions of the sequences areorthogonal to one another, provided, that is, that each cyclic shift,when viewed within the time domain of the transmitted signal, is greaterthan the combined propagation delay and multi-path delay-spread of thattransmitted signal between the transmitter and receiver. In wirelessimplementations, such as MIMO, equalization of several signals, receivedfrom several antennas, is performed to produce one or more equalizeddata streams. Such MIMO operations are more advantageously performedutilizing the Zadoff Chu sequence embodiments described herein, sinceapplication of the present Zadoff Chu sequences to different signalsfrom the different MIMO antennas will assist in matrix construction.

In the exemplary code listed in FIG. 9, the particular set of valuesused for Nzc, u, n1, and n2 (e.g., C code) produces a complex signalwith a constant magnitude in the time domain, and nearly-constant valuesin the frequency domain. Accordingly, Zadoff Chu sequences furtheroperate similarly to a useful training signal that can be used in placeof the pilots that are conventionally used in OFDM. Because of theconstant amplitude property, the Zadoff Chu sequences, the resultanttime domain signal of the sequences has a crest factor of 0 dB, asdescribed above. The present embodiments are therefore of particularlyadvantageous use with respect to power-limited transmitters, such asfound in cellular phones, because the radiated energy for characterizingthe signal path is much greater, while the resulting noise contaminationof the channel estimate is significantly reduced.

FIG. 10 is a graphical illustration depicting a frequency domainspectral plot 1000 of the Zadoff Chu sequence depicted in FIG. 8, andgenerated according to computer program listing 900, FIG. 9. Plot 1000depicts magnitude, real, and imaginary values (y-axis) over frequency(x-axis) of captured spectral data of an FFT of a generated time domainZadoff Chu sequence. Plot 1000 includes a real subplot 1002, andimaginary subplot 1004, and a magnitude subplot 1006. As describedabove, such as Zadoff Chu sequences have ideal autocorrelationfunctions, low crest factors, and relatively flat spectral energy. Thatis, magnitude subplot 1006 remains relatively flat over significantfrequency range, thereby rendering the Zadoff Chu sequence particularlyadvantageous as a channel characterization signal. The Zadoff Chusequence therefore may be used, according to the embodiments describedabove, as a substitute for conventional OFDM pilot signals and trainingsignals. In some embodiments, the spectral energy of the transformedtime domain Zadoff Chu sequence can be created from other values of Nzc,including 127, 255, 511, etc., where Ncz=2{circumflex over ( )}n−1. Asdescribed above, OFDM blocks 814 and 816 were included as portions ofthe previous and subsequent signal, respectively, and each illustratethe time and shape of OFDM time domain energy in a single block. It maybe further noted that the OFDM energy has a large crest factor.

FIG. 11 is a flow chart diagram of an exemplary process 1100 forsimulating an idealized transmitter-receiver chain for an OFDMtransmission having no cyclic prefix (or pilot signals), including anyof the embodiments described above. Process 1100 includes aconfiguration subprocess 1102, and a frequency domain equalizationsubprocess 1104. Process 1100 begins at step 1106 of configurationsubprocess 1102.

In step 1106, process 1100 performs system configuration, includingwithout limitation the symbol time (e.g., 20 μs), the FFT size (e.g.,4096), sub symbol times, the number of sequential OFDM symbols tosimulate (in some cases, process 1100 will discard the first and lastsimulated OFDM symbols). The modulation order (e.g., 1024 QAM) is set.In step 1108, process 1100 performs channel configuration, includingwithout limitation the channel type (e.g., AWGN channel with a singleecho), signal to noise ratio, echo amplitude relative to the directsignal amplitude, and/or echo time delay (e.g., in seconds). In step1110, process 1100 calculates subcarrier values, including withoutlimitation the number of unique complex symbol values, the averagesymbol energy, and/or the average noise energy per subcarriers symbol.

In step 1112, process 1100 generates the transmitted signal. Thegenerated transmitted signal includes generated random symbols for thereal component, and random generated symbols for the imaginarycomponent. In some embodiments, step 1112 includes the further substepsof combining the real and imaginary components, performing an IFFT ofeach symbol to convert to the time domain, and reorganizing into aone-dimensional time sequence. Step 1114, process 1100 generates thechannel, including without limitation a conversion of the echo (in dB)into a linear quantity, and a conversion of the echo delay into asub-symbol index.

In step 1116, process 1100 establishes the channel impulse response. Inan exemplary embodiment, establishing the channel impulse responseincludes substeps of starting with all zero values, adding a 1 value atthe zero-lag tap, and adding the echo at a desired or appropriate tap.In step 1118, process 1100 establishes the noise sequence (e.g., AWGN),and in step 1120, process 1100 calculates the received signal. In anexemplary embodiment, step 1120 includes substeps of convolving thetransmitted signal with a channel impulse response, and trimming theresulting convolution down to its original length and adding the noisesequence thereto.

In step 1122, process 1100 displays the resulting signal as if noequalization had been performed thereupon. In an exemplary embodiment,step 1122 includes the additional sub steps of performing an FFT toconvert the signal to the frequency domain, and plotting theconstellation with associated formatting. Step 1124, process 1100calculates the average subcarrier symbol error energy. In an exemplaryembodiment, step 1124 includes the additional substep of calculating theMER with no equalization. After step 1124, process 1100 proceeds tofrequency domain equalization subprocess 1104.

Frequency domain equalization subprocess 1104 begins at step 1126. Instep 1126, process 1100 pads the channel impulse response to equal twotimes more than the FFT size of the OFDM transmission. In an exemplaryembodiment, step 1126 limits the echo delay to no more than two timesthe FFT size of the OFDM. In step 1128, process 1100 converts thechannel response into the frequency domain.

In step 1130, process 1100 generates overlapping FFT blocks. In anexemplary embodiment, step 1130 generates overlapping FFT blocks thatare two times the FFT size of the OFDM transmission. In step 1132, theoverlapping blocks are converted into the frequency domain. In step1134, the channel response is equalized. In step 1136, the equalizedchannel response is converted back to the time domain. In step 1138, theoverlapping block portions are discarded. In step 1140, the equalizedtime sequence is converted to the frequency domain.

In step 1142, the resulting constellation is plotted and displayed. Instep 1144, additional statistics are displayed with the resultingconstellation, including without limitation the MER, which is calculatedfor each OFDM symbol. According to the example he process of FIG. 11, atransmitter-receiver chain for a digital transmission system issuccessfully simulated to demonstrate implementation, for optimizationpurposes, of the several embodiments described above.

FIG. 12 is a flow chart diagram of an alternative process 1200 forutilizing Zadoff Chu sequences according to the embodiments describedabove. Process 1200 begins at step 1202 in which the receiver (e.g.,receiver 316 or 318, FIG. 3) captures a wireless signal (e.g., signal800, FIG. 8) and stores captured time domain symbols into a memory (notshown in FIG. 3) of the receiver. In step 1204, process 1200 determinesthe frequency offset between the transmitter and receiver from thedetected Zadoff Chu sequences (two Zadoff Chu sequences in the exampledepicted in FIG. 8), and cross-correlates the Zadoff Chu sequences toproduce a peak, and the phase between real and imaginary componentsidentifies the offset frequency.

In step 1206, the captured symbols are de-rotated in the time domain toremove the frequency error from the captured symbols. That is, thereceived complex time domain samples are de-rotated to remove thefrequency offset. In step 1208, the first of the two Zadoff Chusequences is processed to determine the channel response. In at leastone example of step 1208, process 1200 further interpolates thedetermined channel response in the frequency domain. In step 1210,process 1200 utilizes the timing of the cross-correlation peak of theZadoff Chu sequences to identify, or locate, the boundaries of each ofthe 15 OFDM blocks (e.g., blocks 812, FIG. 8).

In step 1212, overlapped compound blocks are formed (e.g., 15 in theexample illustrated in FIG. 8). In at least one example of step 1212,the first and last blocks of the compound blocks include portions of therespective Zadoff Chu sequences, which may be later discarded as neededpseudo-extensions, according to the embodiments described above. In step1214, the compound blocks (e.g., 15) are converted into the frequencydomain by a Fourier transform. In step 1216, frequency domainequalization is performed on each the 15 compound blocks, and then theFDE-equalized blocks are converted into the time domain by an inverseFourier transform. In step 1218, overlapping portions of the equalized,compound time domain blocks are discarded to extract 15 narrow,equalized blocks in the time domain. In step 1220, the extracted narrowblocks are converted into the frequency domain by Fourier transform,after which, the symbols thereof may be sliced and read.

Similar to the embodiments described above, upon completion of step1220, process 1200 may return to step 1202, in which processing isrepeated on the next captured burst, or the next group of previouslycaptured symbols, stored in the receiver memory. As also describedabove, and an optional embodiment, process 1200 may be performed out ofsequence, and/or in near simultaneity, on two or more symbols stored inthe memory.

According to the advantageous systems and methods herein, receiver-basedprocessing techniques may be implemented such that the transmitter mayeliminate cyclic prefixes from multi-carrier digital signaltransmissions. These techniques are thus applicable forequalizing/de-ghosting not only OFDM and OFDMA signals, but also for avariety of other digital transmissions, including without limitationSC-FDMA, single-carrier transmissions, spread spectrum signals, MIMO,and wavelet-based signals.

The techniques of the present embodiments are also particularlyapplicable to transmission systems that utilize pre-distortion, such asupstream DOCSIS 3.1. That is, in such transmission systems, the cyclicprefix may be entirely eliminated from the pre-distorted transmission,which would not generally be processed by the CMTS receiver. DOCSIS 3.0,for example, utilizes pre-distortion for single carrier transmissions,and DOCSIS 3.1 utilizes pre-distortion for OFDMA transmissions. Inconventional examples of these transmission systems, the transmissionsare pre-distorted at the cable modem (CM), and after passing through thelinear distortion of an upstream cable network, arrive at a CMTSreceiver fully equalized. In one illustrative example, a human eye lenspre-distorts an image such that the image will be in generally perfectfocus on the eye retina. In further examples, pre-distortioncoefficients are determined in a training process, referred to as“ranging,” using pilots. According to the embodiments herein, for OFDMAtransmissions, the CP may be eliminated at the CM end, thereby providingup to an additional 25% more upstream throughput. Further to thisexample, no additional equalization processing would be necessary at theCMTS receiver, utilizing the techniques described herein.

As described above, the several embodiments use different types ofoverlapped extensions as pseudo-prefixes/pseudo-suffixes, and thesepseudo-extensions may include one or more of several other types oftransmissions, such as training signals, pilots, signals with othermodulation formats, quiet time, unused or too-short cyclic prefixes, orCAZAC functions/sequences. These pseudo-extensions are multi-functional,and may substitute for cyclic prefixes or other types of guardtransmissions and pilot signals.

Systems and methods according to the present embodiments representfurther significant improvements over conventional transmission schemesby providing dynamically adaptive equalization schemes that allow fordifferent transform sizes to be applied to different signals travelingalong different signal paths of varying lengths. That is, size of an FFTis adjustable for longer echo/reflection delays, as opposed to theshorter path of the direct signal. Similar advantages apply to thedynamically adjustable lengths of the pseudo-extensions as well.

In the case of OFDMA transmissions where multiple transmitters, havingdifferent respective signal paths, contribute to a composite receivedsignal, the frequency domain symbols of each transmitter may beequalized with frequency domain coefficients specifically configured tocorrect for the signal path of that respective transmitter. An exampleof relevant equalization processing is described below with respect toFIGS. 13A-13B.

FIG. 13A is a flow chart diagram of an alternative process 1300 foroperating a receiver, e.g., first receiver 316, FIG. 3, that receivesapproximately simultaneous signals (e.g., composite signal 320) from twodifferent signal paths, e.g., first carrier signal 310(1) and secondcarrier signal 312(1). The respective signal paths of carrier signals310, 312 may be different for a number of reasons, such as due to areflector in one path (e.g., reflecting object 324) that is not in theother path. In this example, first transmitter 302 and secondtransmitter 306 are OFDMA transmitters, no cyclic prefixes are includedin the respective carrier signals.

FIG. 13B is a graphical illustration of alternative frequency plots 1302utilizing an odd-and-even subcarrier scheme 1304 and an upper-and-lowerfrequency band scheme 1306, respectively. In the embodiments illustratedin FIGS. 13A and 13B, receiver 316 is pre-programmed to know whichsubcarriers (A and B, respectively, each OFDMA transmitter 302, 306 isusing. In subcarrier scheme 1304, first transmitter 302 utilizesodd-numbered subcarriers A and second transmitter 306 utilizeseven-numbered subcarriers B. In alternative subcarrier scheme 1306,first transmitter 302 utilizes the lower half of the OFDMA frequencyband, and second transmitter 306 utilizes the upper half of the OFDMAfrequency band.

Referring back to FIGS. 3 and 13A, process 1300 begins at step 1308. Instep 1308, receiver 316 forms a combined (e.g., from composite signal320) compound overlapped block that includes subcarriers from at leasttwo separate transmitters, that is, first transmitter 302 and secondtransmitter 306, in this example. In step 1310, the combined compoundoverlapped block is converted from the time domain into the frequencydomain (e.g., by a Fourier transform or an FFT), and the respectivefrequency domain subcarriers A and B are separated according to whichtransmitter sent the respective subcarriers. The separated frequencydomain subcarrier symbols are then processed similarly, but separately,as follows.

In step 1312, FDE is applied to the symbols from both of the A and Bsubcarriers using equalization coefficients corresponding to each of therespective signal paths 310(1) and 312(1). In step 1314, the equalized Aand B symbols are converted, separately, into the time domain (e.g., byan inverse Fourier transform or IFFT). In an embodiment, for the Asubcarriers, a value of zero may be inserted for all subcarriers from B,and similarly, for the B subcarriers, a value of zero may be insertedfor all subcarriers from A. In step 1316, still in the time domain, theoverlapped portions (pseudo-extensions) of the equalized and convertedcomposite A and B blocks are discarded to create two separate narrow Aand B blocks. Step 1318 is an optional step, which may be implemented inthe case where the processed symbols are from an OFDMA transmission. Inan example of step 1318, the narrow A and B blocks are transformed againinto the frequency domain (e.g., by Fourier transform, FFT) and thesymbols are read.

The techniques of FIGS. 13A-B are further advantageous with respect toSC-FDMA transmissions that do not utilize cyclic prefixes. In suchcases, where the input signal is SC-FDMA, optional step 1318 would notbe needed. The present embodiments are particular useful in the case ofmultiple transmissions of different types. That is, for example, wherefirst transmitter 302 implements an OFDMA transmission and secondtransmitter 306 implements an SC-FDMA transmission, receiver 316 isconfigured to receive a composite signal containing different A and Bsubcarriers, and then separately process the respective symbols thereof.In this example, optional step 1318 would be implemented to read thesymbols of the narrow A blocks (OFDMA), but would not need to beimplemented for the narrow B blocks (SC-FDMA). This could happen, forexample, if B blocks came from a battery-powered device, and A blockscame from a device connected to the AC power supply, and was nottherefore power-constrained.

Thus, in the case of a composite signal having multiple transmissions,which may or may not individually include cyclic prefixes, the cyclicprefixes become irrelevant. The significant factor will be the durationof the reflections (e.g., the longest echo) among the multipletransmissions. More importantly, where cyclic prefixes are implemented,the duration of a cyclic prefix for particular transmission would not beexpected to change for the particular carrier in which it isimplemented. Echoes and reflections, on the other hand, are subject tochange from path to path, and over time within a single path. Accordingto the present embodiments though, a receiver can be configured todynamically adjust, in real-time, the length of theoverlap/pseudo-extensions according to the conditions that are actuallyencountered.

U.S. Pat. No. 5,886,749 describes a system where repeated energy (anNTSC horizontal sync signal) is used to enable an overlapped transformwith FDE. The present embodiments advantageously utilize a periodicallyrepeated ZC sequence instead of the NTSC sync signal to more reliablyenable an overlapped transform with FDE. Nevertheless, as describedabove, the present embodiments avoid the need for repeated (e.g.,cyclic) energy. The present systems and methods advantageously utilizeenergy adjacent to the target block, such as an adjacent block itself,which does not affect the equalized target block because the adjacentsignal portions are discarded after processing.

Further advantages of the present embodiments become readily apparent inthe case where one transmitter's signal arrives early or late relativeto the other transmitter's signal. If there was a timing offset betweenthe start of the A block and the B block, this timing offset would beautomatically corrected by the FDE subprocess, because the time shiftwill appear as a rotation in the frequency domain correctioncoefficients.

The present embodiments offer still further advantages with respect tothe use of the present Zadoff Chu sequences as training signals. Thatis, equalization of conventional OFDM or OFDMA blocks is moreeffectively executed by substituting a CAZAC functions/Zadoff Chusequences for pilot subcarriers. According to the present embodiments,even when the substitute (ZC) training signal is shorter in durationthan the compound block that is intended to be transformed and equalizedin the frequency domain, the frequency domain coefficients maynevertheless be interpolated in order to equalize the overlappedfrequency domain extensions.

In some embodiments, in the case of a series of OFDMA blocktransmissions, the present systems and methods advantageously allow foruse of the cyclic prefix (or quiet time) on the first block on the firsttransmitter, so that the first transmitter is protected from a previoussignal echo from another signal path. Successive blocks from this firsttransmitter may then advantageously omit the use of the cyclic prefix,thereby saving significant transmission time for substantive data.

The present embodiments that eliminate cyclic prefixes from digitaltransmission signals are still further useful beyond simply reducingtransmission time to improve system efficiency. Indeed, the presentembodiments are particularly valuable for implementations where thelength of echoes on a signal path render the use of cyclic prefiximpractical, thereby limiting the types of transmission schemes that maybe utilized on such signal paths. For example, in the case of aparticular signal path having a duration of 50 μs for its longest echo,and for a maximum allowed overhead of 10%, the OFMD symbol period wouldhave to be greater than 500 μs. A 500 μs symbol, however, would requirean inordinately expensive precision local oscillator. Such precisionlocal oscillators become even more costly at very high frequencies, suchas millimeter wave frequencies (e.g., 60 GHz). According to the presentsystems and methods though, by eliminating the need for cyclic prefixes,OFDM transmission technology may be implemented on this exemplary signalpath without requiring such costly hardware outlays.

Duobinary Modulation for OFDM Transmission

Duobinary modulation is a transmission scheme for transmitting N baudusing a bandwidth of less than capital N/2 Hz. However, since theminimum bandwidth required of a transmitted pulse is N/2 Hz, adjacentduobinary pulses experience ISI. A data communication system thatimplements duobinary modulation includes a duobinary encoder, whichimplements the duobinary code from original symbols, and a duobinarydecoder, which recovers the original symbols from the duobinary signal.

The duobinary decoding process is prone to error propagation, since anestimate of a given sample relies on the estimate of previous sample.One conventional technique to mitigate this error propagation implementsa precoder before the duobinary encoder at the transmitter.

However, when duobinary coding is applied in the frequency domain,conventional encoding that is designed for sequential time-domainduobinary signals are known to experience compromised efficiency.Accordingly, it is desirable to create an improved encoder design foruse with frequency domain duobinary OFDM transmissions.

In an exemplary embodiment of duobinary transmission, a datacommunication system has a total number N of OFDM subcarriers. Becauseof the duobinary modulation scheme, the number of independentsubcarriers carrying original symbols will then be N−1. At thetransmitter side of the communication system, the duobinary encoding canbe expressed as:

y=Ax  (Eq. 1)

Where x=(x₁, x₂, . . . x_(N-1))^(T) and represents a vector includingthe N−1 original or precoded symbols, y=(y₁, y₂, . . . y_(N))^(T) andrepresents a vector including the N duobinary OFDM subcarriers, and A isa N×(N−1) matrix. Matrix A can be further expressed according to:

$\begin{matrix}{A = {\begin{pmatrix}I_{N - 1} \\0\end{pmatrix} + \begin{pmatrix}0 \\I_{N - 1}\end{pmatrix}}} & ( {{Eq}.\mspace{14mu} 2} )\end{matrix}$

Where I_(N-1) constitutes a (N−1)×(N−1) identical matrix.

In one example, where the total number of subcarriers is 4, three of thesubcarriers are independent, and will contain QPSK symbols 1+j, 1−j, and−1+j. Thus, the duobinary encoding that will correspond to (Eq. 1) canbe expressed as:

$\begin{matrix}{y = {{Ax} = {{\begin{pmatrix}1 & \; & \; \\1 & \; & \; \\\; & 1 & \; \\\; & 1 & \; \\\; & \; & 1 \\\; & \; & 1\end{pmatrix}\mspace{11mu} \begin{pmatrix}{1 + j} \\{1 - j} \\{{- 1} + j}\end{pmatrix}} = \begin{pmatrix}{1 + j} \\2 \\0 \\{{- 1} + j}\end{pmatrix}}}} & ( {{Eq}.\mspace{14mu} 5} )\end{matrix}$

FIG. 14 is a graphical illustration depicting a comparative overlay 1400of an OFDM sinc function implementing a duobinary technique according tothe present embodiments. In the example illustrated in FIG. 14, onesubcarrier 1402 is shown, and represents a sinc function (samplingfunction) in the frequency domain. Implementing a duobinary operation onsubcarrier 1402, a copy 1404 of subcarrier 1402 is obtained, but havinga frequency shift of pi (π). A combination subcarrier 1406 is thenobtained by combining subcarrier 1402 with copy 1404. Combinationsubcarrier 1406 can then be seen to have significantly reducedsidelobes, as compared with subcarrier 1402 and copy 1404, because therespective sidelobes values of subcarrier 1402 and copy 1404substantially cancel each other out at all sidelobes. This example isparticularly illustrative of how the present embodiments implementduobinary modulation on OFDM transmissions to significantly reduce theOOB leakage in comparison with a conventional OFDM transmission. Thesignificant improvement realized by the present embodiments over theconventional techniques is further illustrated with respect to FIG. 15.

Duobinary OFDM represents an innovative modulation technique that has acharacteristic of low adjacent channel interference with respect toneighboring frequencies. As described further below with respect toFIGS. 17A-B, the energy of a conventional single symbol is spreadbetween two adjacent symbols. In the time domain, this spread creates anOFDM symbol with a half-cosine envelope. In the frequency domain though,the spectrum is rectangular, with low OOB interference. In an exemplaryembodiment, this duobinary OFDM symbol is transmitted without a cyclicprefix, and then be demodulated with a CP-elimination receiver(described above). In an alternative embodiment, the duobinary OFDMsymbol may be demodulated by a conventional OFMD receiver, and a CP canbe optionally added.

In the case where a CP is added to the duobinary OFDM symbol, the timedomain waveform envelope takes on the shape of a “fish” (describedfurther below with respect to FIGS. 17A-B), and some of the OOBperformance will then be compromised by the abrupt drop of the “tail” ofthe fish. Duobinary processing is conventionally done with a filterhaving an impulse response extending over two symbols. In at least oneembodiment, OOB leakage of the OFMD transmission may be reducedutilizing raised cosine tapering in the time domain, however, thisalternative method will result in an increased transmission time. Raisedcosine tapering is used, for example, in the DOCSIS 3.1 modulationstandard.

FIG. 15 is a graphical illustration depicting a comparative overlay 1500of a duobinary OFDM block transmission 1502 with a conventional OFDMblock transmission 1504. As can be seen from overlay 1500, an amount ofadjacent channel interference 1506 (dark shaded area) from duobinaryOFDM block transmission 1502 is significantly reduced with respect to anamount of adjacent channel interference 1508 (light shaded area) ofconventional OFDM. The present duobinary techniques thus provide adramatic improvement with respect to conventional OFDM transmissions. Inthe example shown in FIG. 15, the vertical scale per division is 10 dB.

In some embodiments, the crest factor (see FIG. 17A, below) may bereduced by interleaving the upper and lower sidebands in the timedomain. That is, while the lower sideband is going to zero, the uppersideband is cresting, and vice versa. Additionally, the principlesdescribed herein are not limited to only the example shown, but may bealso advantageously implemented for modulation formats without uniformsubcarrier amplitudes, including but not limited to 64-QAM.

Furthermore, the duobinary modulation techniques of the presentembodiments represent only one example of the new modulation method thatis created by interchanging time and frequency axes of signal duals. Inan exemplary embodiment, adaptation techniques from single carrier tomulticarrier utilize a 90 degree rotation in a time-frequency plot.

A duality between time and frequency exists, which can be observed fromdiscrete Fourier transform and discrete inverse Fourier transformequations (see e.g., Eqs. 6 and 7, below). Differences between suchequations typically involve only a scale factor and a negative sign infront of the complex exponential. Substantively, the equations are quitesimilar. Given a set a transform pairs, it is often difficult toidentify which graph of a plotted signal is a time domain plot, andwhich is a frequency domain plot.

For example, with a single carrier signal, such as a pulse amplitudemodulation (PAM), each symbol is considered to be short in time, butwide in bandwidth, and having a next symbol occurring sequentially intime. An OFDM subcarrier, on the other hand, is considered to be narrowin frequency, but long in duration. Additionally, many OFDM subcarriersoperate simultaneously in time. An illustrative comparison of these twoexemplary signal types is shown below with respect to FIG. 16.

FIG. 16 is a graphical illustration depicting a block time-frequencyplot 1600. In this example, plot 1600 is illustrated as a 32×32 block of32 PAM single carrier symbols 1602 (a single PAM symbol illustrated forease of explanation) extending in the time direction (vertical) and 32multicarrier OFDM symbols 1604 (a single OFDM symbol also illustrated).That is, all 32 PAM symbols 1602 are time domain symbols in the rowdirection, and can be transmitted in time over the duration of a singleOFDM symbol 1604. Similarly, all 32 OFDM symbols 1604 are frequencydomain symbols in the column direction, and can fit within the bandwidthof a single PAM symbol 1602. As can therefore be seen from FIG. 16, a 90degree rotation of plot 1600 (visually, about the plot “center point”)demonstrates the present modulation technique that effectively turns thePAM transmission into an OFDM transmission, and vice versa.

By this modulation technique, a 32×1 symbol can be mathematicallyrotated to become a 1×32 symbol, and vice versa. This principle may beexpanded, for example, to rotate a plurality of time division multipleaccess (TDMA) single carrier sequential transmissions, from a pluralityof transmitters, to effectively obtain a plurality of OFDMA simultaneoustransmissions from the plurality of transmitters. Furthermore, althoughOFDM (without time domain tapering, e.g., raised cosine) exhibits OOBenergy splatter, this characteristic is analogous to the sin(x)/xresponse (in time) of PAM signals if the channel rolloff factor (alpha)is small, or zero (the “brick wall”). Therefore, according to thisembodiment, an OFDM transmission utilizing time domain tapering willperform an operation analogous to a PAM transmission utilizing aroll-off factor. This rotational illustration of the present modulationtechniques demonstrates still further advantages that may be realizedover conventional duobinary transmissions, as illustrated below withrespect to FIGS. 17A-B.

FIG. 17A is a graphical illustration depicting a time domain plot 1700of a duobinary block transmission, and FIG. 17B is a graphicalillustration depicting a frequency domain plot 1702 of the duobinaryblock transmission depicted in FIG. 17A. As illustrated in FIG. 17A,time domain plot 1700 generally includes an envelope shaped like ahalf-cosine. When time domain plot 1700 is rotated 90 degrees, a“conventional” duobinary result is produced, and the time axis can thenbe relabeled as “frequency.”. This rotational modulation technique, whenperformed on a conventional duobinary transmission, is referred toherein as “FD duobinary” or “duobinary OFDM.” As illustrated in FIG.17B, frequency domain plot 1702 is substantially flat, and exhibits anabrupt drop of OOB energy, which is desirable to reduce interferencewith the neighboring channels.

In some embodiments, the present FD duobinary modulation techniques maybe implemented with respect to an OFDM transmission utilizing cyclicprefixes. An optional cyclic prefix 1704 is illustrated in FIG. 17A, andrepresents the front portion of the envelope of time domain plot 1700being utilized as a CP. When cyclic prefix 1704 is so utilized, thesine-shaped envelope of the time domain duobinary signal resembles theshape of a fish, with cyclic prefix 1704 observable as the “tail” of the“fish.” As described further below, the use of cyclic prefixes with thepresent FD duobinary modulation techniques is optional, and unnecessarywhen implementing a “no-CP receiver” according to the embodimentsdescribed above. When a cyclic prefix is not so implemented, the“fishtail” of time domain plot 1700 disappears, but the frequency domainplot 1702 improves, as the abrupt drop of the fishtail causes some OOBleakage.

As can be seen with respect to frequency domain plot 1702, threedifferent power levels are visible: (i) the peak subcarrier level (flatportion); (ii) an intermediate subcarrier level (drop off portions); and(iii) a zero-power subcarrier level (where the energy drops to theorigin). In conventional time domain duobinary implementations, theoccupied bandwidth of a QPSK signal, relative to partial responsesignaling (PRS, or 9-PRS), is greater according to the channel roll-offfactor, alpha. For DOCSIS single carrier modulations, this bandwidthincrease is approximately 5% greater for the downstream transmission andapproximately 25% greater for the upstream transmission. According tothe present FD duobinary techniques though, if the number of subcarriersis the same, with equal subcarrier spacing, the occupied bandwidth willremain the same, and not experience this increase. This bandwidthadvantage occurs as result of the FD duobinary techniques producing themore abrupt drop of OOB energy (see e.g., FIG. 15), which therebyenables closer carrier spacing.

The FD duobinary modulation techniques of the present embodimentsdemonstrate a time-frequency swapping technique that advantageouslyrelates OFDM and single carrier modulation transmissions as duals of oneanother, after the respective time and frequency axes are rotated and“relabeled.” This time-frequency swapping technique allows newmodulation candidates to be created, such as duobinary (e.g., PRS) OFDM,which has valuable properties for the cable plant.

Conventional modulation techniques are used at carrier frequencies tosend digital data over a distance, either by wires, wireless, oroptically. Three known modulation techniques include single carrier,multi-carrier, and code division multiple access (CDMA). All threetechniques have been used on cable networks at one time or another.

The orthogonality between signals is a property that allows one signal,which includes a plurality of symbols, to be clearly received withoutinterference from the symbols of another signal. This orthogonality canbe expressed, for example, according to the following equation:

Σx(n)*y(n)=0  (Eq. 7)

Where the variables, x and y, are orthogonal over a range if the sum ofall x*y products are equal to zero over a range where y≠x. Where thesignals represent complex numbers, for example, (Eq. 7) would considerthe sum of all x*conj(y) products. Different modulation techniques areknown to achieve orthogonality by other means or calculations. Acomparative example of impulse and resulting spectral responses areillustrated below with respect to FIGS. 18A-D, for a single carrier QPSKtransmission and a duobinary 9-PRS transmission

FIG. 18A is a graphical illustration depicting an impulse response 1800of the single carrier transmission. FIG. 18B is a graphical illustrationdepicting a spectral response 1802 of the single carrier transmissiondepicted in FIG. 18A. FIG. 18C is a graphical illustration depicting animpulse response 1804 of a conventional duobinary transmission (e.g., animpulse response of 1.0 for two symbols, in this example). FIG. 18D is agraphical illustration depicting a spectral response 1806 of theduobinary transmission depicted in FIG. 18C. As illustrated in FIG. 18A,a basic modulation technique, such as BPSK, can be created by connectinga periodic series of positive or negative impulses to a lowpass filter(not shown) having a sine(x)/x impulse response (see also FIG. 14,above). A raised cosine frequency response on the modulated signal maythen be produced therefrom, as represented by spectral response 1802 ofFIG. 18B. The abruptness of the frequency domain roll-off, asillustrated in FIG. 18B, represents the “alpha” factor, and is affectedby damping applied to the sine(x)/x waveform.

In contrast, duobinary modulation employees a different impulseresponse, as illustrated by duobinary impulse response 1804 of FIG. 18C.In comparison with impulse response 1800 of the single carriertransmission (FIG. 18A), duobinary impulse response can be seen to lastover two symbol periods, as opposed to one symbol period, as illustratedin FIG. 18C. Moreover, the frequency domain of the resultant spectralresponse 1806, FIG. 18D, has a cosine shape, as opposed to the raisedcosine shape of spectral response 1802 of the single carriertransmission.

FIG. 19A is a graphical illustration of a constellation 1900 depictingrelative power calculations for error thresholds of the QPSK singlecarrier transmission depicted in FIGS. 18A-B, and FIG. 19B is agraphical illustration of a constellation 1902 depicting relative powercalculations for error thresholds of the 9-PRS duobinary transmissiondepicted in FIGS. 18C-D. The 9-PRS signal may be produced, for example,by passing a two-level complex (i.e., I and Q) signal through aduobinary filter (not shown in FIG. 19B).

As illustrated in FIG. 19A, the QPSK signal has four equally probablestates, whereas, as illustrated in FIG. 19B, the 9-PRS signal has asingle state (middle of plot) having a probability of 0.25, fourhigh-power corner states with a combined probability of 0.25 (i.e.,0.0625 each), and four intermediate power levels between the cornershaving a combined probability of 0.5 (i.e., 0.125 each). Thus, if thevoltage difference between points A and B on constellation 1902 isassumed to be 1.0V, the power of the 9-PRS constellation will be0.25*0+0.5*1.0+0.25*1.414{circumflex over ( )}2=1 watt. In comparison,if the voltage difference on the QPSK constellation 1900 is set to be0.707V between points C and D, the QPSK power it will also be 1 watt.Accordingly, a noise vector that would be required to make a slicingerror on the QPSK signal will be 0.707V, whereas 0.5V would be requiredfor the 9-PRS signal, resulting in a difference of 3 dB between the twoconstellations. This difference is realized for the duobinarytransmission over the QPSK signal by taking advantage of the fact thatnot all states are equally probable for the duobinary signal, despitethe fact that both signals have a same RF power.

FIG. 20 is a graphical illustration depicting a diagram 2000 of singlecarrier voltage versus time. Diagram 2000 is comparable to overlay 1400,FIG. 14, and impulse response 1800, FIG. 18A. In cable systems, singlecarrier modulation, e.g., 64-QAM and 256-QAM, has been used extensivelyon downstream signal paths, and upstream signal paths have utilizedadvanced time division multiple access (ATDMA), which is essentially aburst-mode single carrier transmission technique. Single carriermodulation includes a time series of voltage impulses (symbols) thathave been filtered to limit interference with other frequency bands.Diagram 2000 thus illustrates five different sine(x)/x impulses withuniform time shifts. That is, five different symbols represented ondiagram 2000 have a same value, but are shifted in time with respect toone another.

In operation, the symbols of diagram 2000 may have any positive ornegative values, and/or have real-only values or include complex values.The vertical lines appearing in diagram 2000 represent five separatesampling instants. The five separate waveforms are not considered tointerfere with each other because, at each sampling instant, aparticular symbol reaches its peak the value (1), while the othersymbols are passing through zero. Accordingly, orthogonality ismaintained throughout diagram 2000. In further operation, the systemrepresented by diagram 2000 may be optimized to remove lineardistortions, such as echoes, prior to sampling (e.g., using an adaptiveequalizer). Without such optimization, the responses from the otherrespective symbols may not be zero at the particular sampling instant.In such instances, the non-zero symbols may contribute to distortionenergy to the selected symbol.

FIG. 21 is a graphical illustration depicting a timing diagram 2100 fora spread spectrum signal. Direct sequence spread spectrum (DSSS)technology has been used in military applications to hide or maskcommunications and radar signals by making the signals appearnoise-like. A related technology, known as synchronous code divisionmultiple access (S-CDMA), has been used in cable transmission systems toprovide upstream noise immunity, and for multiple accessimplementations. In an exemplary embodiment, timing diagram 2100includes a low speed data input 2102, a pseudo-noise (PN) sequence 2104,an output 2106, and a chip rate 2108.

In the example illustrated in FIG. 21, multiple orthogonal codes areassigned to one or more users, and simultaneous transmissions may thusoccur on different codes without interference. In an exemplaryembodiment, the DSSS/S-CDMA technique of timing diagram 2100 furtherutilizes equalized signals to prevent loss of orthogonality betweencodes. In operation, a low speed data input 2102 is clocked againsthigh-speed PN sequence 2104 (e.g., by use of an exclusive-OR gate, shownbelow with respect to FIG. 22) to produce output 2106, which appearsnoise-like. Further operation of timing diagram 2100 is explainedfurther below with respect to FIG. 22.

FIG. 22 is a schematic illustration depicting an exemplary block diagramof a system 2200 for direct sequence spread transmission and reception.System 2200 includes a transmitter portion 2202 and a receiver portion2204, and is configured to implement operation of timing diagram 2100,FIG. 21. In operation of system 2200, a random PN sequence (i.e., PNsequence 2104) is created using a plurality of cascading shift registers2206 and an exclusive-OR gate 2208. The clocking rate of the severalcomponents represents chip rate 2108. A signal to be transmitted, i.e.,output 2106, is generated by a data source inverting or not inverting,i.e., through implementation of exclusive-OR gate 2208, thepseudo-random output (PN sequence 2104) of shift registers 2206. Atreceiver portion 2204, a PN generator 2210 synchronizes with transmitterportion 2202, and also uses the same code (PN sequence 2104) toreproduce the signal of low speed data input 2102. Where system 2200includes S-CDMA DOCSIS functionality, each circular time shift by shiftregisters 2206 (excluding the initial chip, which would not the shifted)produces another basis function that is orthogonal to all other shifts.In at least one embodiment, system 2200 further implements a pre-coder(not shown in FIG. 22), as described above, to eliminate errorpropagation at receiver portion 2204, as well as the FD duobinary OFDMtechniques also described above. In some embodiments, receiver portion2204 is configured to consider only one received symbol at a time.

Referring back to FIG. 2A-B, OFDM is used in DOCSIS 3.1 technology, aswell as in many wireless standards. Some OFDM implementations obtainorthogonality through further utilization of different subcarriers thatare all harmonics of the same fundamental. FIG. 2A is an illustrativeexample of an OFDM waveform with only four such subcarriers. Each of theharmonically-related subcarriers depicted in the illustration has adifferent magnitude and phase value from each other. When all foursubcarriers are combined (i.e., summed) for transmission, the result isa single composite signal. However, orthogonality allows the originalsubcarriers to be separated at the receiver, typically using an FFT.Accordingly, FIG. 2B as an illustrative example of the same OFDM signalof FIG. 2A, but shown in the frequency domain.

FIG. 23 is a graphical illustration depicting a plot 2300 of a receivedOFDM signal in the frequency domain. Specifically, plot 2300 representsa spectral plot of an OFDM signal that is affected by a deepfrequency-selective fade. This fading phenomenon occurs frequently inwireless channels where a sum of echo components cancels the signalentirely, or at least at some subcarrier frequencies (e.g., the secondharmonic carrier HC2, in the example illustrated in FIG. 23).Accordingly, the techniques and principles of the present embodimentsare particularly applicable to such OFDM environments, where fadedsubcarriers that are essentially lost in the noise floor may berecovered using forward error correction (FEC) operations.

FIG. 24 is a graphical illustration of a plot 2400 depicting time andfrequency relationships between common transmission impairments. Plot2400 is particularly illustrative when considered together withtime-frequency plot 1600, FIG. 16, above. Plot 2400 illustrates therelative effects from common transmission impairments in both the timedomain and the frequency domain. As illustrated in FIG. 24, plot 2400enables the visual understanding of the various effects from thedifferent impairments on the different types of modulation.

For example, plot 2400 illustrates how random thermal, or Gaussian,noise is present at all frequencies and all times, and thus there is nopresent modulation technique that has a relative advantage to addressadditive white Gaussian noise (AWGN). The maximum data capacity in achannel having AWGN can be determined, for example, according to theShannon Hartley Theorem. If the noise is not white noise (i.e., thespectrum of the noise is not flat), the maximum capacity of the channelmay be determined according to the “water-pour” method of transmit powerdistribution. In cable systems, having a non-flat SNR may result fromcable loss varying with frequency, as well as nonlinear distortionproducts, which are random noise-like if the distortion was created bydigital carriers.

Plot 2400 further illustrates that burst noise come on the other hand,occurs locally in time, but often has a wide spectrum. Single carriermodulation, with FEC, may therefore be effective to address burst noisein order to correct corrupted time domain symbols. However, it should benoted that a typical OFDM receiver will perform an FFT on the corruptedsequence, and thus spread the burst noise contamination to all relatedfrequency domain symbols. In contrast, plot 2400 illustrates that acontinuous wave (CW) interference source may be continuous in time, butrelatively localized in frequency. OFDM modulation techniques having FECmight be utilized to repair such localized damage, to a limited numberof subcarriers. However, use of single carrier modulation with a CWinterferer will affect all symbols, thereby turning a constellationpoint (see e.g., FIGS. 19A-B) into a “donut” shape. Plot 2400 stillfurther illustrates that a deep frequency-selective fade may beaddressed in a similar manner as with CW interference, namely, by OFDMmodulation with FEC.

There are other important considerations for selecting a modulationtechnique for a particular RF signal path, such as (i) tolerance tofrequency offsets and tolerance to phase noise, both of which increasethe cost of local oscillators, and (ii) peak-to-average power ratio,which makes transmitters consume more power, thereby decreasing batterylife. Additionally, some receiver designers are known to furtherimplement a number of design tricks, sometimes referred to as “secretsauces,” to mitigate the effects of impairments, such as noisecancelers.

In consideration of the embodiments described above, a signal E fortransmission, includes a plurality of individual component symbolse_(n), and may be represented as follows:

E=└e ₁ ,e ₂ ,e ₃ ,e ₄ . . . e _(j)┘  (Eq. 8)

For this signal E, a modulation matrix C may be formulated. Themodulation matrix C includes rows and columns, and is optimallyconfigured such that the respective rows are orthogonal to one another.Accordingly, in this mathematical representation, each of the threemodulation techniques described above can be seen as essentiallyrepresenting merely a different set of row functions, which are alsoreferred to as orthogonal basis functions. For single carriermodulation, the modulation matrix C may constitute simply an identitymatrix having a single diagonal row of 1s and 0s elsewhere. (See e.g.,Eq. 5, above). For a DSSS signal modulation, the respective rows may beprovided from a Walsh matrix, implementing a single circular shiftbetween rows.

The modulation matrix C may also include complex components, which maybe represented as follows:

$\begin{matrix}{C = \begin{bmatrix}{c( {1,1} )} & {c( {1,2} )} & . & . & . & {c( {1,k} )} \\{c( {2,1} )} & {c( {2,2} )} & . & . & . & {c( {2,k} )} \\{c( {3,1} )} & {c( {3,2} )} & . & . & . & {c( {3,k} )} \\. & . & . & . & . & . \\. & . & . & . & . & . \\. & . & . & . & . & . \\{c( {j,1} )} & {c( {j,2} )} & . & . & . & {c( {j,k} )}\end{bmatrix}} & ( {{Eq}.\mspace{14mu} 9} )\end{matrix}$

The general principle of orthogonality between rows may then berestated, for all rows where x≠y, according to:

Σ_(n=1) ^(n=k) c(x,n)c(y,n)=0  (Eq. 10)

Accordingly, the unmodulated signal E may be transmitted as a modulatedsignal F by multiplying the input sequence of the unmodulated signal Eby the modulation matrix C, represented by:

F=E*C=└f ₁ ,f ₂ ,f ₃ ,f ₄ . . . f _(j)┘  (Eq. 11)

With respect to OFDM modulation, the respective rows of the modulationmatrix C may also represent complex exponentials (e.g., sine and cosinewaves), where the first row would represent, for example, the firstharmonic, the second row would represent the second harmonic, etc., asillustrated below with respect to FIG. 25.

FIG. 25 is a graphical illustration depicting an OFDM modulation matrix2500. FIG. 25 is a graphical illustration depicting an OFDM modulationmatrix 2500. In the example illustrated in FIG. 25, modulation matrix2500 is an eight-row matrix of signs and cosines for an OFDM modulation,where the cosine waves are depicted as solid lines, and the sine wavesare depicted as dashed lines. Further in this example, row X[1] isdepicted to form an upper sideband, and row X[7] is depicted to form amatching lower sideband.

The innovative principles of the embodiments described aboveadvantageously coordinate the time and frequency relationships betweentransmitted symbols to effectively render single carrier modulation andmulticarrier OFDM modulation as separate aspects of the same modulationtechnique, wherein the separate aspects are distinguished by a 90-degreerotation in the time-frequency plot.

The duality between time and frequency according to the presentembodiments can be further observed in consideration of the followingdiscrete Fourier transform (DFT) and inverse discrete Fourier transform(IDFT) equations:

$\begin{matrix}{{f\lbrack k\rbrack} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{F\lbrack n\rbrack}e^{{+ j}\frac{2\pi}{N}{nk}}}}}} & ( {{Eq}.\mspace{14mu} 12} ) \\{{F\lbrack k\rbrack} = {\sum\limits_{k = 0}^{N - 1}{{f\lbrack k\rbrack}e^{{- j}\frac{2\pi}{N}{nk}}}}} & ( {{Eq}.\mspace{14mu} 13} )\end{matrix}$

That is, the essential differences between these two equations are thescale factor and the polarity sign in front of the complex exponential.The equations are otherwise very similar. Observing only a plotted setof transform pairs, for example, it would be difficult to identify whichplot represents time and which represents frequency, as illustratedabove in time-frequency plot 1600, FIG. 16. Without knowing therotational frame of reference, that is, which axis represents time andwhich axis represents frequency, the PAM transmission is essentiallyindistinguishable from the OFDM transmission.

In some cases, non-orthogonal signals are utilized for communicationtransmissions. For example, a non-orthogonal spread-spectrum signal mayoperate in the presence of other signal types by taking advantage ofspreading gain. In such instances, some level of interference will beexperienced with the non-orthogonal signal, however, such interferenceis optimally kept within tolerable levels.

According to the rotational principles of the modulation techniquesdescribed above, the same symbol may be observed as either a 32×1 symbolor as a 1×32 symbol, depending on the rotational frame of reference. Itshould be noted though, that dispersion, or other linear distortion,occurs along the time axis, but not along the frequency axis. Dispersionalong the frequency axis would be instead indicate non-lineardistortion. Thus, according to the embodiments described herein,performing a 90 degree rotation on a particular sequence is effectivelythe same as performing a FFT on that sequence. Similarly, performance ofa −90 degree rotation on the particular sequence effectivelyaccomplishes an IFFT on that sequence. Thus, the rotational operationsof the present embodiments may be implemented using FFTs and IFFTs (orDFTs and IDFTs, respectively).

Referring back to FIGS. 17A-B, the desirable characteristic of a gentlerise and fall in transmit power level is a result of duobinarymodulation summing each subcarrier with in an adjacent subcarrier, wherethat the adjacent subcarrier has a same magnitude component. Theduobinary OFDM modulation techniques of the present embodiments are ofparticular advantage with respect to very narrow bandwidth OFDMtransmissions having a relatively small number of subcarriers, e.g.,Internet of Things (IoT), ham radio operation, etc. The techniquesdescribed herein effectively resolve the spectral splatter experiencedin such environments, which cause adjacent channel interference. Thepresent embodiments are also of particular use in signaling operationsthat utilize a small number of bits in a narrow bandwidth, such as“acks” or acknowledgements.

The present embodiments may also be implemented with respect toconventional pre-coding techniques (see e.g., “Digital Telephony,” 3dEd, by John Bellamy), which allow allows a symbol to be decoded withoutreferencing a preceding symbol (e.g., correlative level encoding). Theduobinary OFDM techniques herein are described, by way of example, for2-level I and Q signals (QPSK), which are illustrated to be convertedinto a 3×3 constellation. The person of ordinary skill in the artthough, will understand that these examples are provided forillustration purposes, and are not intended to be limiting. According tothe principles described herein, the present embodiments may beimplemented with respect to other modulation orders. A 16-QAM modulationorder, for example, when duobinary-filtered, will create a 49-pointconstellation.

The duobinary modulation techniques of this description may also utilizeimpulse responses other than those with 2 adjacent symbols. For example,an impulse response according to the present embodiments include morethan 2 symbols. In other instances, where two symbols are utilized, the2 symbols need not be on adjacent subcarriers

As described above, time-frequency duals are conventionally known, butthe modulation techniques thereof are conventionally considered to beseparate from one another. That is, OFDM is considered to be the dual ofthe single carrier, and OFDMA is considered to be the dual of singlecarrier TDMA, but the conventional modulation techniques therefor areconsiderably different from one another.

Windowed OFDM to Reduce ISI and GOB Emissions

As described above, a raised cosine function may be produced on thespectral response of some of the embodiments. In an exemplaryembodiment, an alternative process applies a time domain windowfunction, such as a Hamming window, to reduce ISI and OOB emissions.

FIG. 26A is a graphical illustration depicting a Hamming window function2600 in the time domain. FIG. 26B is a graphical illustration depictingan inverse Hamming function 2602 in the time domain. FIG. 26C is agraphical illustration depicting an implementation of a Hamming windowon a time domain waveform 2604. In the exemplary embodiment, the timedomain window function utilizes Hamming window functions according tothe examples shown in FIGS. 26A-C.

In operation, the time domain window function is applied to an OFDM orOFDMA waveform, and the windowed waveform therefrom is then transmitted.The implementation of the window function will create some ISI, butreduce the OOB emissions. However, the window function may be selected,as described below, to cancel the created ISI in the frequency domainwith a frequency domain convolution, as described below with respect toFIGS. 27A-B. Implementation of the windowing/window function operationmay be performed at either or both of the transmitter and the receiverof the system.

FIG. 27A is a graphical illustration depicting a Hamming impulseresponse 2700 in the frequency domain. FIG. 27B is a graphicalillustration depicting an inverse convolution impulse response 2702 inthe frequency domain. In operation, by reversing the Hamming window(i.e., inverting in time domain, for example, by inverse Hammingfunction 2602, FIG. 26B) any noise-plus-interference that occurs may bemultiplied while a transmitted signal is weak. In an exemplaryembodiment, this problem may be alleviated by implementing a maximumlikelihood estimation for the frequency domain symbols, based upon theknowledge of what the original Hamming impulse response (e.g., impulseresponse 2700) looks like, as illustrated below with respect to FIGS.28A-B. In this exemplary embodiment, ISI created utilizing a Hammingimpulse response 2700 may be corrected through frequency domainconvolution with an inverse filter H(f), representing inverseconvolution impulse response 2702.

FIG. 28A is a graphical illustration depicting an unequalizedconstellation 2800 on which a Hamming window (e.g., Hamming windowfunction 2600, FIG. 26A) has been implemented. FIG. 28B is a graphicalillustration depicting an equalized constellation 2802 on which aHamming window has been implemented. Unequalized constellation 2800demonstrates the effect of the created ISI and OOB emissions on thetransmission from applying only the time domain window function withoutfurther correction. Equalized constellation 2802 demonstrates how thecreated ISI and OOB emissions can be corrected through the coordinatedfrequency domain equalization techniques described above, whichimplement the inverse impulse response of the selected time domainwindow function, or Hamming window.

FIG. 29A is a graphical illustration depicting an implementation of araised cosine voltage function on a time domain waveform 2900. FIG. 29Bis a graphical illustration depicting an unequalized constellation 2902on which a raised cosine function has been implemented. FIG. 29C is agraphical illustration depicting a constellation 2904, afterequalization, on which a raised cosine function has been implemented.FIGS. 29A-C illustrate, by way of comparison, the significantimprovement in windowing presented by the present techniques, ascompared with conventional raised cosine operations. The resultingconstellations produced according to the present techniques may be muchmore carefully controlled than with implementation of the raised cosinewindow, which, although exhibiting more uniform power, will alsoexperience the “division-by-zero” problem in its inverse time response.

According to these embodiments, ISI damage to the waveform can be moreeasily repaired, and performed with significantly improved precision.These advantageous techniques have particular applicability to cabletransmission operations, where, for example, one OFDM signal may becresting, while another OFDM signal is passing through a minimum power.OFDM signals, for example, constitute orthogonal basis functions, whichinclude sines and cosines, each having an integer number of cycles. Thebasis functions must be orthogonal to prevent energy leakage intoneighboring signals. The present embodiments advantageously implement atime domain Hamming function on the time domain waveform of the OFDMsignal, but in the frequency domain, utilize a Hamming impulse response,and inverse impulse response for convolution.

In an exemplary embodiment, the Hamming window is implemented on a QPSKOFDMA transmission exhibiting ISI. Implementation of the time domainwindowing operation/Hamming window results in significant reduction inan amount of leakage from adjacent blocks, while also reducing OOBsplatter. In at least one embodiment, implementation of the Hammingwindow is made more uniform through utilization of a second carrier outof phase.

Although specific features of various embodiments may be shown in somedrawings and not in others, this is for convenience only. In accordancewith the principles of the systems and methods described herein, anyfeature of a drawing may be referenced or claimed in combination withany feature of any other drawing. For example, the following list ofexample claims represents only some of the potential combinations ofelements possible from the systems and methods described herein.

a(i). A signal equalizing receiver, configured to: capture a pluralityof OFDM symbols transmitted over a signal path adding linear distortionto the plurality of OFDM symbols; form the plurality of captured OFDMsymbols into an overlapped compound data block, wherein the compounddata block includes at least one pseudo-extension in addition to payloaddata from at least one of the plurality of OFDM symbols; process theoverlapped compound data block with one of (i) a circular convolutionhaving an inverse channel response in the time domain, and (ii) afrequency domain equalization in the frequency domain, to produce anequalized compound block; discard at least one end portion of theequalized compound block to produce a narrow equalized block, whereinthe at least one end portion corresponds with the at least onepseudo-extension, and wherein the narrow equalized block correspondswith the payload data; and cascade two or more narrow equalized blocksto form a de-ghosted signal stream of the plurality of OFDM symbols,wherein the plurality of OFDM symbols includes one or more of an OFDMtransmission and an OFDMA transmission, wherein the plurality of OFDMsymbols includes one or more of a cyclic prefix and no cyclic prefix,and wherein a length of the at least one pseudo-extension is differentthan a length of the cyclic prefix.

a(ii). A digital transmission receiver having a processor and a memory,configured to: receive a digital signal transmission from a signal pathincluding a plurality of data blocks having linear distortion;determine, from the signal path of the digital signal transmission, aduration of at least one reflection of the digital signal transmissionon the digital signal path; attach a pseudo-extension to a first datablock of the plurality of data blocks, wherein the length of thepseudo-extension in the time domain is greater than the duration of theat least one reflection; process the first data block, together with thepseudo-extension attached thereto, to remove linear distortion from thefirst data block; and discard the processed pseudo-extension from theprocessed first data block after the linear distortion has been removed.

b(ii). The receiver of claim a(ii), wherein the signal path includes afirst signal subpath and second signal subpath different from the firstsignal subpath.

c(ii) The receiver of claim b(ii), wherein the first signal subpath is awired subpath and the second signal subpath is a wireless subpath.

d(ii) The receiver of claim b(ii), wherein the first signal subpath is adirect signal path and the second signal subpath is an indirect signalpath.

e(ii). The receiver of claim b(ii), wherein the reflection istransmitted along the second signal subpath.

f(ii). The receiver of claim b(ii), wherein the second signal subpath islonger than the first signal subpath.

g(ii). The receiver of claim b(ii), wherein the receiver is furtherconfigured to receive (i) a real component of the digital signaltransmission from the first signal subpath, and (ii) an imaginarycomponent of the digital signal transmission from the second signalsubpath.

h(ii) The receiver of claim a(ii), wherein the receiver is furtherconfigured to process the first data block using an overlapped circularconvolution process.

i(ii). The receiver of claim a(ii), wherein the receiver is furtherconfigured to process the first data block using an overlapped Fouriertransform process.

j(ii). The receiver of claim a(ii), wherein the pseudo-extensioncomprises at least one of a pseudo-prefix obtained from a second datablock preceding the first data block, and a pseudo-suffix obtained froma third data block succeeding the first data block.

k(ii). The receiver of claim a(ii), wherein the receiver is furtherconfigured to process the digital signal transmission from one or moredigital transmission schemes, including orthogonal frequency-divisionmultiplexing (OFDM), orthogonal frequency-division multiple-access(OFDMA), data over cable service interface specification (DOCSIS),multiple input/multiple output (MIMO), and single-carrierfrequency-division multiple-access (SC-FDMA).

a(iii). A digital transmission system, comprising: a transmitterconfigured to transmit orthogonal frequency-division multiplexing (OFDM)symbols having no cyclic prefix attached thereto; a receiver forreceiving the transmitted OFDM symbols from the transmitter; and asignal path for communicating the transmitted OFDM symbols from thetransmitter to the receiver, wherein the OFDM symbols received by thereceiver include linear distortion from the signal path, and wherein thereceiver is configured to process the received OFDM symbols and lineardistortion using an overlapped circular convolution function to produceequalized OFDM symbols.

a(iv). A digital transmission system, comprising: a transmitterconfigured to transmit orthogonal frequency-division multiplexing (OFDM)symbols having no cyclic prefix attached thereto; a receiver forreceiving the transmitted OFDM symbols from the transmitter; and asignal path for communicating the transmitted OFDM symbols from thetransmitter to the receiver, wherein the OFDM symbols received by thereceiver include linear distortion from the signal path, wherein thereceiver is configured to process the received OFDM symbols and lineardistortion by an overlapped Fourier transform function to produceequalized OFDM symbols, and wherein the overlapped Fourier transformfunction is configured to (i) overlap individual ones of the distortedOFDM symbols with overlapped time energy from respectively adjacent onesof the distorted OFDM symbols, (ii) transform the overlapped individualdistorted OFDM symbols into distorted frequency domain symbols, (iii)perform complex multiplication of the distorted frequency domain symbolsby equalization coefficients to equalize the distorted frequency domainsymbols, (iv) remove the overlapped time energy from a time domaincomponent of the equalized frequency domain symbols, and (v) produceundistorted frequency domain symbols from a frequency domain componentof the time domain component with the overlapped time energy removed.

a(v). A digital transmission system, comprising: a transmitterconfigured to transmit (i) a series of orthogonal frequency-divisionmultiplexing (OFDM) symbols having no cyclic prefix attached thereto,and (ii) at least one constant amplitude zero autocorrelation waveformsequence (CAZAC) sequence; a receiver for receiving the transmittedseries of OFDM symbols and the CAZAC sequence from the transmitter; anda signal path for communicating the transmitted series of OFDM symbolsand CAZAC sequence from the transmitter to the receiver, wherein theseries of OFDM symbols and the CAZAC sequence are received by thereceiver with linear distortion from the signal path, and wherein thereceiver is configured to utilize the received CAZAC sequence as areference signal for equalizing the received series of OFDM symbols.

b(v). The system of claim a(v), wherein the CAZAC sequence comprises atleast one Zadoff Chu sequence.

c(v). The system of claim b(v), wherein the at least one Zadoff Chusequence comprises a first Zadoff Chu sequence preceding the series ofOFDM symbols in the time D and a second Zadoff Chu sequence succeedingthe series of OFDM symbols in the time domain.

d(v). The system of claim a(v), wherein the receiver is furtherconfigured to determine from the received CAZAC sequence at least one ofa channel characterization, an offset frequency, and a start of one ormore of the OFDM symbols in the time domain.

a(vi). A method of equalizing a transmitted digital signal, comprisingthe steps of: receiving, in the time domain, a sequential series offirst, second, and third data blocks of the transmitted digital signal;forming a compound block in the time domain from the second data blockincluding an end portion of first data block and a leading portion ofthe third data block; performing circular convolution on the compoundblock using a set of equalization coefficients to equalize the compoundblock in the time domain; extracting from the equalized compound block anarrow block corresponding to equalized time domain data of the seconddata block; converting the narrow block from the time domain intofrequency domain data; and reading frequency domain symbols relating tothe second data block from the converted narrow block.

b(vi). The method of claim a(vi), further comprising a step of forming acompound block in the time domain from the third data block including anend portion of second data block and a leading portion of a fourth datablock immediately succeeding the third data block.

c(vi) The method of claim a(vi), wherein the transmitted digital signalis an orthogonal frequency-division multiplexing (OFDM) signal, andwherein the frequency domain symbols are OFDM symbols.

a(vii). A method of equalizing a digital signal transmitted over asignal path, comprising the steps of: receiving, in the time domain, asequential series of time domain samples of the transmitted digitalsignal; forming the received sequential series of time domain samplesinto a separate sub-series of overlapping compound time domain blocks,wherein each compound time domain block of the sub-series includes apseudo-prefix comprising information from an immediately precedingblock; determining an echo delay on the signal path; converting thecompound blocks into the frequency domain to form compound frequencydomain blocks; equalizing the compound frequency domain blocks to formequalized frequency domain blocks; converting the equalized frequencydomain blocks into the time domain to form equalized time domaincompound blocks; discarding, from the equalized time domain compoundblocks, overlapping time domain energy portions corresponding torespective equalized pseudo-prefixes, to form narrow equalized blocks;pasting the narrow equalized blocks together to form a compositeequalized time domain signal; and converting the composite equalizedtime domain into the frequency domain and read equalized frequencydomain symbols therefrom.

b(vii) The method of claim a(vii), wherein the digital signal is anorthogonal frequency-division multiplexing (OFDM) signal, and whereinthe equalized frequency domain symbols are OFDM symbols.

c(vii). The method of claim a(vii), wherein the step of determiningcomprises one of (i) performing signal characterization for the signalpath and (ii) assigning a pre-determined threshold value for the echodelay.

a(viii). A method of modulating, by a transmitter, a series of inputdigital symbols of a first modulation scheme, comprising the steps of:receiving a sequential series of samples of the digital symbols in afirst domain of the first modulation scheme, wherein the first domain isone of the time domain and the frequency domain; determining a dual ofthe first modulation scheme, wherein the dual has a second modulationscheme in a second domain that is different from the first domain, andwherein the second domain comprises the other of the time domain and thefrequency domain; applying a 90 degree rotational operation to thesecond modulation scheme to generate a rotational modulation format;modulating the series of digital symbols with the generated rotationalmodulation format; and outputting the modulated series of digitalsymbols to a receiver.

b(viii). The method of claim a(viii), wherein the first modulationscheme comprises a single carrier modulation scheme.

c(viii). The method of claim b(viii), wherein the single carriermodulation scheme comprises quadrature amplitude modulation.

d(viii). The method of claim b(viii), wherein the single carriermodulation scheme comprises pulse amplitude modulation.

e(viii) The method of claim d(viii), wherein the second modulationscheme comprises orthogonal frequency division multiplexing modulation.

f(viii). The method of claim b(viii), wherein the orthogonal frequencydivision multiplexing modulation comprises partial response signaling.

g(viii). The method of claim a(viii), wherein the first modulationscheme comprises orthogonal frequency division multiple accessmodulation, and wherein the second modulation scheme comprises timedivision multiple access modulation.

h(viii). The method of claim a(viii), wherein the first modulationscheme comprises a multicarrier modulation format, and wherein thesecond modulation scheme comprises a single carrier modulation format.

i(viii). The method of claim a(viii), wherein the first modulationscheme comprises one of a spread spectrum modulation format and a codedivision multiple access format.

j(viii). The method of claim a(viii), further comprising a step ofequalizing the series of digital symbols prior to the step ofmodulating.

k(viii) The method of claim a(viii), further comprising a step ofprecoding the series of digital symbols prior to the step of modulating.

l(viii). The method of claim a(viii), wherein the generated rotationalmodulation format comprises one of binary phase shift keying andduobinary modulation.

m(viii). The method of claim a(viii), wherein the step of applyingcomprises one of a Fourier transform operation and an inverse Fouriertransform operation.

a(ix). A digital transmission system, comprising: a transmitterconfigured to transmit an input series of complex symbols; a duobinaryencoder disposed within the transmitter, and configured to filter theinput series of complex symbols and output a partial response signaling(PRS) signal; a converter disposed within the transmitter, andconfigured to convert the PRS signal output into the time domain; and areceiver for receiving the time domain-converted PRS signal from thetransmitter over a signal path.

b(ix). The system of claim a(ix), wherein the transmitter furthercomprises a pre-coder configured to pre-code the complex symbols priorto filtering by the duobinary encoder.

c(ix). The system of claim a(ix), wherein the converter is furtherconfigured to perform at least one of a fast Fourier transform, aninverse fast Fourier transform, a discrete Fourier transform, and aninverse discrete Fourier transform.

d(ix) The system of claim a(ix), wherein the signal path comprises atleast one of a cable network, a wired transmission line, a wirelesspath, and a fiber optic line.

e(ix). The system of claim a(ix), wherein the complex symbols comprisean orthogonal frequency division multiple access symbols transmitted inan upstream direction of the digital transmission system.

f(ix). The system of claim a(ix), wherein the converter is furtherconfigured to construct a duobinary OFDM signal for transmission bysplitting a subcarrier of the input series of complex symbols to appearover two adjacent frequency domain subcarriers.

a(x). A method of modulating, by a transmitter, an input digital signaltransmission, comprising the steps of: receiving the input digitalsignal having a first time-frequency order on the time-frequency axis;rotating the time-frequency axis by 90 degrees; modulating the inputdigital signal according to the rotated time-frequency axis; andoutputting the modulated digital signal to a receiver.

Some embodiments involve the use of one or more electronic or computingdevices. Such devices typically include a processor, processing device,or controller, such as a general purpose central processing unit (CPU),a graphics processing unit (GPU), a microcontroller, a reducedinstruction set computer (RISC) processor, an application specificintegrated circuit (ASIC), a programmable logic circuit (PLC), aprogrammable logic unit (PLU), a field programmable gate array (FPGA), adigital signal processing (DSP) device, and/or any other circuit orprocessing device capable of executing the functions described herein.The methods described herein may be encoded as executable instructionsembodied in a computer readable medium, including, without limitation, astorage device and/or a memory device. Such instructions, when executedby a processing device, cause the processing device to perform at leasta portion of the methods described herein. The above examples areexemplary only, and thus are not intended to limit in any way thedefinition and/or meaning of the term processor and processing device.

This written description uses examples to disclose the embodiments,including the best mode, and also to enable any person skilled in theart to practice the embodiments, including making and using any devicesor systems and performing any incorporated methods. The patentable scopeof the disclosure is defined by the claims, and may include otherexamples that occur to those skilled in the art. Such other examples areintended to be within the scope of the claims if they have structuralelements that do not differ from the literal language of the claims, orif they include equivalent structural elements with insubstantialdifferences from the literal language of the claims.

We claim:
 1. A method of modulating, by a transmitter, a series of inputdigital symbols of a first modulation scheme, comprising the steps of:receiving a sequential series of samples of the digital symbols in afirst domain of the first modulation scheme, wherein the first domain isone of the time domain and the frequency domain; determining a dual ofthe first modulation scheme, wherein the dual has a second modulationscheme in a second domain that is different from the first domain, andwherein the second domain comprises the other of the time domain and thefrequency domain; applying a 90 degree rotational operation to thesecond modulation scheme to generate a rotational modulation format;modulating the series of digital symbols with the generated rotationalmodulation format; and outputting the modulated series of digitalsymbols to a receiver.
 2. The method of claim 1, wherein the firstmodulation scheme comprises a single carrier modulation scheme.
 3. Themethod of claim 2, wherein the single carrier modulation schemecomprises quadrature amplitude modulation.
 4. The method of claim 2,wherein the single carrier modulation scheme comprises pulse amplitudemodulation.
 5. The method of claim 4, wherein the second modulationscheme comprises orthogonal frequency division multiplexing modulation.6. The method of claim 2, wherein the orthogonal frequency divisionmultiplexing modulation comprises partial response signaling.
 7. Themethod of claim 1, wherein the first modulation scheme comprisesorthogonal frequency division multiple access modulation, and whereinthe second modulation scheme comprises time division multiple accessmodulation.
 8. The method of claim 1, wherein the first modulationscheme comprises a multicarrier modulation format, and wherein thesecond modulation scheme comprises a single carrier modulation format.9. The method of claim 1, wherein the first modulation scheme comprisesone of a spread spectrum modulation format and a code division multipleaccess format.
 10. The method of claim 1, further comprising a step ofequalizing the series of digital symbols prior to the step ofmodulating.
 11. The method of claim 1, further comprising a step ofprecoding the series of digital symbols prior to the step of modulating.12. The method of claim 1, wherein the generated rotational modulationformat comprises one of binary phase shift keying and duobinarymodulation.
 13. The method of claim 1, wherein the step of applyingcomprises one of a Fourier transform operation and an inverse Fouriertransform operation.
 14. A digital transmission system, comprising: atransmitter configured to transmit an input series of complex symbols; aduobinary encoder disposed within the transmitter, and configured tofilter the input series of complex symbols and output a partial responsesignaling (PRS) signal; a converter disposed within the transmitter, andconfigured to convert the PRS signal output into the time domain; and areceiver for receiving the time domain-converted PRS signal from thetransmitter over a signal path.
 15. The system of claim 14, wherein thetransmitter further comprises a pre-coder configured to pre-code thecomplex symbols prior to filtering by the duobinary encoder.
 16. Thesystem of claim 14, wherein the converter is further configured toperform at least one of a fast Fourier transform, an inverse fastFourier transform, a discrete Fourier transform, and an inverse discreteFourier transform.
 17. The system of claim 14, wherein the signal pathcomprises at least one of a cable network, a wired transmission line, awireless path, and a fiber optic line.
 18. The system of claim 14,wherein the complex symbols comprise an orthogonal frequency divisionmultiple access symbols transmitted in an upstream direction of thedigital transmission system.
 19. The system of claim 14, wherein theconverter is further configured to construct a duobinary OFDM signal fortransmission by splitting a subcarrier of the input series of complexsymbols to appear over two adjacent frequency domain subcarriers.
 20. Amethod of modulating, by a transmitter, an input digital signaltransmission, comprising the steps of: receiving the input digitalsignal having a first time-frequency order on the time-frequency axis;rotating the time-frequency axis by 90 degrees; modulating the inputdigital signal according to the rotated time-frequency axis; andoutputting the modulated digital signal to a receiver.